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annotate +sbp/+implementations/d2_variable_4.m @ 266:bfa130b7abf6 operator_remake

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Added error message for too few grid points to all implementation files.
author Martin Almquist <martin.almquist@it.uu.se>
date Fri, 09 Sep 2016 11:03:13 +0200
parents 6009f2712d13
children f7ac3cd6eeaa
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [H, HI, D1, D2, e_l, e_r, d_l, d_r] = d2_variable_4(m,h)
266
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
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2
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
3 BP = 4;
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
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4 if(m<2*BP)
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
6 end
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
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7
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8 N = m;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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9
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
10 H = speye(N);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
11 H(1,1) = 17/48; H(2,2) = 59/48; H(3,3) = 43/48; H(4,4) = 49/48;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 H(N,N) = 17/48; H(N-1,N-1) = 59/48; H(N-2,N-2) = 43/48; H(N-3,N-3) = 49/48;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
13 H = h*H;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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14
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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15 HI = inv(H);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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16
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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17 H = sparse(H);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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18 HI = sparse(HI);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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19
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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20
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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21 S = sparse(N,N);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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22 S(1,1:4) = 1/h*[(-11/6);3;(-3/2);1/3];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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23 S(N,N-3:N) = 1/h*[(-1/3);3/2;(-3);11/6];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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24 S = sparse(S);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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25
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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26 e_l = sparse(m,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 e_l(1) = 1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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28
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 e_r = sparse(m,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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30 e_r(end) = 1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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31
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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32 d_l = S(1,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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33 d_r = S(end,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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34
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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35 e=ones(m,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36 Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
37 Q_U = [0 0.59e2 / 0.96e2 -0.1e1 / 0.12e2 -0.1e1 / 0.32e2; -0.59e2 / 0.96e2 0 0.59e2 / 0.96e2 0; 0.1e1 / 0.12e2 -0.59e2 / 0.96e2 0 0.59e2 / 0.96e2; 0.1e1 / 0.32e2 0 -0.59e2 / 0.96e2 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
38 Q(1:4,1:4)=Q_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
39 Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
41 D1=HI*(Q-1/2*e_l*e_l'+1/2*e_r*e_r') ;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43 function D2 = D2_fun(c)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
44 M = 78+(N-12)*5;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
45 %h = 1/(N-1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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46
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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47
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
48 U = [48/(17)*(0.12e2 / 0.17e2 * c(1) + 0.59e2 / 0.192e3 * c(2) + 0.27010400129e11 / 0.345067064608e12 * c(3) + 0.69462376031e11 / 0.2070402387648e13 * c(4)) 48/(17)*(-0.59e2 / 0.68e2 * c(1) - 0.6025413881e10 / 0.21126554976e11 * c(3) - 0.537416663e9 / 0.7042184992e10 * c(4)) 48/(17)*(0.2e1 / 0.17e2 * c(1) - 0.59e2 / 0.192e3 * c(2) + 0.213318005e9 / 0.16049630912e11 * c(4) + 0.2083938599e10 / 0.8024815456e10 * c(3)) 48/(17)*(0.3e1 / 0.68e2 * c(1) - 0.1244724001e10 / 0.21126554976e11 * c(3) + 0.752806667e9 / 0.21126554976e11 * c(4)) 48/(17)*(0.49579087e8 / 0.10149031312e11 * c(3) - 0.49579087e8 / 0.10149031312e11 * c(4)) 48/(17)*(-c(4) / 0.784e3 + c(3) / 0.784e3);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
49 48/(59)*(-0.59e2 / 0.68e2 * c(1) - 0.6025413881e10 / 0.21126554976e11 * c(3) - 0.537416663e9 / 0.7042184992e10 * c(4)) 48/(59)*(0.3481e4 / 0.3264e4 * c(1) + 0.9258282831623875e16 / 0.7669235228057664e16 * c(3) + 0.236024329996203e15 / 0.1278205871342944e16 * c(4)) 48/(59)*(-0.59e2 / 0.408e3 * c(1) - 0.29294615794607e14 / 0.29725717938208e14 * c(3) - 0.2944673881023e13 / 0.29725717938208e14 * c(4)) 48/(59)*(-0.59e2 / 0.1088e4 * c(1) + 0.260297319232891e15 / 0.2556411742685888e16 * c(3) - 0.60834186813841e14 / 0.1278205871342944e16 * c(4)) 48/(59)*(-0.1328188692663e13 / 0.37594290333616e14 * c(3) + 0.1328188692663e13 / 0.37594290333616e14 * c(4)) 48/(59)*(-0.8673e4 / 0.2904112e7 * c(3) + 0.8673e4 / 0.2904112e7 * c(4));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
50 48/(43)*(0.2e1 / 0.17e2 * c(1) - 0.59e2 / 0.192e3 * c(2) + 0.213318005e9 / 0.16049630912e11 * c(4) + 0.2083938599e10 / 0.8024815456e10 * c(3)) 48/(43)*(-0.59e2 / 0.408e3 * c(1) - 0.29294615794607e14 / 0.29725717938208e14 * c(3) - 0.2944673881023e13 / 0.29725717938208e14 * c(4)) 48/(43)*(c(1) / 0.51e2 + 0.59e2 / 0.192e3 * c(2) + 0.13777050223300597e17 / 0.26218083221499456e17 * c(4) + 0.564461e6 / 0.13384296e8 * c(5) + 0.378288882302546512209e21 / 0.270764341349677687456e21 * c(3)) 48/(43)*(c(1) / 0.136e3 - 0.125059e6 / 0.743572e6 * c(5) - 0.4836340090442187227e19 / 0.5525802884687299744e19 * c(3) - 0.17220493277981e14 / 0.89177153814624e14 * c(4)) 48/(43)*(-0.10532412077335e14 / 0.42840005263888e14 * c(4) + 0.1613976761032884305e19 / 0.7963657098519931984e19 * c(3) + 0.564461e6 / 0.4461432e7 * c(5)) 48/(43)*(-0.960119e6 / 0.1280713392e10 * c(4) - 0.3391e4 / 0.6692148e7 * c(5) + 0.33235054191e11 / 0.26452850508784e14 * c(3));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
51 48/(49)*(0.3e1 / 0.68e2 * c(1) - 0.1244724001e10 / 0.21126554976e11 * c(3) + 0.752806667e9 / 0.21126554976e11 * c(4)) 48/(49)*(-0.59e2 / 0.1088e4 * c(1) + 0.260297319232891e15 / 0.2556411742685888e16 * c(3) - 0.60834186813841e14 / 0.1278205871342944e16 * c(4)) 48/(49)*(c(1) / 0.136e3 - 0.125059e6 / 0.743572e6 * c(5) - 0.4836340090442187227e19 / 0.5525802884687299744e19 * c(3) - 0.17220493277981e14 / 0.89177153814624e14 * c(4)) 48/(49)*(0.3e1 / 0.1088e4 * c(1) + 0.507284006600757858213e21 / 0.475219048083107777984e21 * c(3) + 0.1869103e7 / 0.2230716e7 * c(5) + c(6) / 0.24e2 + 0.1950062198436997e16 / 0.3834617614028832e16 * c(4)) 48/(49)*(-0.4959271814984644613e19 / 0.20965546238960637264e20 * c(3) - c(6) / 0.6e1 - 0.15998714909649e14 / 0.37594290333616e14 * c(4) - 0.375177e6 / 0.743572e6 * c(5)) 48/(49)*(-0.368395e6 / 0.2230716e7 * c(5) + 0.752806667e9 / 0.539854092016e12 * c(3) + 0.1063649e7 / 0.8712336e7 * c(4) + c(6) / 0.8e1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52 0.49579087e8 / 0.10149031312e11 * c(3) - 0.49579087e8 / 0.10149031312e11 * c(4) -0.1328188692663e13 / 0.37594290333616e14 * c(3) + 0.1328188692663e13 / 0.37594290333616e14 * c(4) -0.10532412077335e14 / 0.42840005263888e14 * c(4) + 0.1613976761032884305e19 / 0.7963657098519931984e19 * c(3) + 0.564461e6 / 0.4461432e7 * c(5) -0.4959271814984644613e19 / 0.20965546238960637264e20 * c(3) - c(6) / 0.6e1 - 0.15998714909649e14 / 0.37594290333616e14 * c(4) - 0.375177e6 / 0.743572e6 * c(5) 0.8386761355510099813e19 / 0.128413970713633903242e21 * c(3) + 0.2224717261773437e16 / 0.2763180339520776e16 * c(4) + 0.5e1 / 0.6e1 * c(6) + c(7) / 0.24e2 + 0.280535e6 / 0.371786e6 * c(5) -0.35039615e8 / 0.213452232e9 * c(4) - c(7) / 0.6e1 - 0.13091810925e11 / 0.13226425254392e14 * c(3) - 0.1118749e7 / 0.2230716e7 * c(5) - c(6) / 0.2e1;...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53 -c(4) / 0.784e3 + c(3) / 0.784e3 -0.8673e4 / 0.2904112e7 * c(3) + 0.8673e4 / 0.2904112e7 * c(4) -0.960119e6 / 0.1280713392e10 * c(4) - 0.3391e4 / 0.6692148e7 * c(5) + 0.33235054191e11 / 0.26452850508784e14 * c(3) -0.368395e6 / 0.2230716e7 * c(5) + 0.752806667e9 / 0.539854092016e12 * c(3) + 0.1063649e7 / 0.8712336e7 * c(4) + c(6) / 0.8e1 -0.35039615e8 / 0.213452232e9 * c(4) - c(7) / 0.6e1 - 0.13091810925e11 / 0.13226425254392e14 * c(3) - 0.1118749e7 / 0.2230716e7 * c(5) - c(6) / 0.2e1 0.3290636e7 / 0.80044587e8 * c(4) + 0.5580181e7 / 0.6692148e7 * c(5) + 0.5e1 / 0.6e1 * c(7) + c(8) / 0.24e2 + 0.660204843e9 / 0.13226425254392e14 * c(3) + 0.3e1 / 0.4e1 * c(6)];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
54
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
55
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
56 L = [c(N-7) / 0.24e2 + 0.5e1 / 0.6e1 * c(N-6) + 0.5580181e7 / 0.6692148e7 * c(N-4) + 0.4887707739997e13 / 0.119037827289528e15 * c(N-3) + 0.3e1 / 0.4e1 * c(N-5) + 0.660204843e9 / 0.13226425254392e14 * c(N-2) + 0.660204843e9 / 0.13226425254392e14 * c(N-1) -c(N-6) / 0.6e1 - 0.1618585929605e13 / 0.9919818940794e13 * c(N-3) - c(N-5) / 0.2e1 - 0.1118749e7 / 0.2230716e7 * c(N-4) - 0.13091810925e11 / 0.13226425254392e14 * c(N-2) - 0.13091810925e11 / 0.13226425254392e14 * c(N-1) -0.368395e6 / 0.2230716e7 * c(N-4) + c(N-5) / 0.8e1 + 0.48866620889e11 / 0.404890569012e12 * c(N-3) + 0.752806667e9 / 0.539854092016e12 * c(N-2) + 0.752806667e9 / 0.539854092016e12 * c(N-1) -0.3391e4 / 0.6692148e7 * c(N-4) - 0.238797444493e12 / 0.119037827289528e15 * c(N-3) + 0.33235054191e11 / 0.26452850508784e14 * c(N-2) + 0.33235054191e11 / 0.26452850508784e14 * c(N-1) -0.8673e4 / 0.2904112e7 * c(N-2) - 0.8673e4 / 0.2904112e7 * c(N-1) + 0.8673e4 / 0.1452056e7 * c(N-3) -c(N-3) / 0.392e3 + c(N-2) / 0.784e3 + c(N-1) / 0.784e3;...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
57 -c(N-6) / 0.6e1 - 0.1618585929605e13 / 0.9919818940794e13 * c(N-3) - c(N-5) / 0.2e1 - 0.1118749e7 / 0.2230716e7 * c(N-4) - 0.13091810925e11 / 0.13226425254392e14 * c(N-2) - 0.13091810925e11 / 0.13226425254392e14 * c(N-1) c(N-6) / 0.24e2 + 0.5e1 / 0.6e1 * c(N-5) + 0.3896014498639e13 / 0.4959909470397e13 * c(N-3) + 0.8386761355510099813e19 / 0.128413970713633903242e21 * c(N-2) + 0.280535e6 / 0.371786e6 * c(N-4) + 0.3360696339136261875e19 / 0.171218627618178537656e21 * c(N-1) -c(N-5) / 0.6e1 - 0.4959271814984644613e19 / 0.20965546238960637264e20 * c(N-2) - 0.375177e6 / 0.743572e6 * c(N-4) - 0.13425842714e11 / 0.33740880751e11 * c(N-3) - 0.193247108773400725e18 / 0.6988515412986879088e19 * c(N-1) -0.365281640980e12 / 0.1653303156799e13 * c(N-3) + 0.564461e6 / 0.4461432e7 * c(N-4) + 0.1613976761032884305e19 / 0.7963657098519931984e19 * c(N-2) - 0.198407225513315475e18 / 0.7963657098519931984e19 * c(N-1) -0.1328188692663e13 / 0.37594290333616e14 * c(N-2) + 0.2226377963775e13 / 0.37594290333616e14 * c(N-1) - 0.8673e4 / 0.363014e6 * c(N-3) c(N-3) / 0.49e2 + 0.49579087e8 / 0.10149031312e11 * c(N-2) - 0.256702175e9 / 0.10149031312e11 * c(N-1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 48/(49)*(-0.368395e6 / 0.2230716e7 * c(N-4) + c(N-5) / 0.8e1 + 0.48866620889e11 / 0.404890569012e12 * c(N-3) + 0.752806667e9 / 0.539854092016e12 * c(N-2) + 0.752806667e9 / 0.539854092016e12 * c(N-1)) 48/(49)*(-c(N-5) / 0.6e1 - 0.4959271814984644613e19 / 0.20965546238960637264e20 * c(N-2) - 0.375177e6 / 0.743572e6 * c(N-4) - 0.13425842714e11 / 0.33740880751e11 * c(N-3) - 0.193247108773400725e18 / 0.6988515412986879088e19 * c(N-1)) 48/(49)*(c(N-5) / 0.24e2 + 0.1869103e7 / 0.2230716e7 * c(N-4) + 0.507284006600757858213e21 / 0.475219048083107777984e21 * c(N-2) + 0.3e1 / 0.1088e4 * c(N) + 0.31688435395e11 / 0.67481761502e11 * c(N-3) + 0.27769176016102795561e20 / 0.712828572124661666976e21 * c(N-1)) 48/(49)*(-0.125059e6 / 0.743572e6 * c(N-4) + c(N) / 0.136e3 - 0.23099342648e11 / 0.101222642253e12 * c(N-3) - 0.4836340090442187227e19 / 0.5525802884687299744e19 * c(N-2) + 0.193950157930938693e18 / 0.5525802884687299744e19 * c(N-1)) 48/(49)*(0.260297319232891e15 / 0.2556411742685888e16 * c(N-2) - 0.59e2 / 0.1088e4 * c(N) - 0.106641839640553e15 / 0.1278205871342944e16 * c(N-1) + 0.26019e5 / 0.726028e6 * c(N-3)) 48/(49)*(-0.1244724001e10 / 0.21126554976e11 * c(N-2) + 0.3e1 / 0.68e2 * c(N) + 0.752806667e9 / 0.21126554976e11 * c(N-1));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59 48/(43)*(-0.3391e4 / 0.6692148e7 * c(N-4) - 0.238797444493e12 / 0.119037827289528e15 * c(N-3) + 0.33235054191e11 / 0.26452850508784e14 * c(N-2) + 0.33235054191e11 / 0.26452850508784e14 * c(N-1)) 48/(43)*(-0.365281640980e12 / 0.1653303156799e13 * c(N-3) + 0.564461e6 / 0.4461432e7 * c(N-4) + 0.1613976761032884305e19 / 0.7963657098519931984e19 * c(N-2) - 0.198407225513315475e18 / 0.7963657098519931984e19 * c(N-1)) 48/(43)*(-0.125059e6 / 0.743572e6 * c(N-4) + c(N) / 0.136e3 - 0.23099342648e11 / 0.101222642253e12 * c(N-3) - 0.4836340090442187227e19 / 0.5525802884687299744e19 * c(N-2) + 0.193950157930938693e18 / 0.5525802884687299744e19 * c(N-1)) 48/(43)*(0.564461e6 / 0.13384296e8 * c(N-4) + 0.470299699916357e15 / 0.952302618316224e15 * c(N-3) + 0.550597048646198778781e21 / 0.1624586048098066124736e22 * c(N-1) + c(N) / 0.51e2 + 0.378288882302546512209e21 / 0.270764341349677687456e21 * c(N-2)) 48/(43)*(-0.59e2 / 0.408e3 * c(N) - 0.29294615794607e14 / 0.29725717938208e14 * c(N-2) - 0.2234477713167e13 / 0.29725717938208e14 * c(N-1) - 0.8673e4 / 0.363014e6 * c(N-3)) 48/(43)*(-0.59e2 / 0.3136e4 * c(N-3) - 0.13249937023e11 / 0.48148892736e11 * c(N-1) + 0.2e1 / 0.17e2 * c(N) + 0.2083938599e10 / 0.8024815456e10 * c(N-2));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
60 48/(59)*(-0.8673e4 / 0.2904112e7 * c(N-2) - 0.8673e4 / 0.2904112e7 * c(N-1) + 0.8673e4 / 0.1452056e7 * c(N-3)) 48/(59)*(-0.1328188692663e13 / 0.37594290333616e14 * c(N-2) + 0.2226377963775e13 / 0.37594290333616e14 * c(N-1) - 0.8673e4 / 0.363014e6 * c(N-3)) 48/(59)*(0.260297319232891e15 / 0.2556411742685888e16 * c(N-2) - 0.59e2 / 0.1088e4 * c(N) - 0.106641839640553e15 / 0.1278205871342944e16 * c(N-1) + 0.26019e5 / 0.726028e6 * c(N-3)) 48/(59)*(-0.59e2 / 0.408e3 * c(N) - 0.29294615794607e14 / 0.29725717938208e14 * c(N-2) - 0.2234477713167e13 / 0.29725717938208e14 * c(N-1) - 0.8673e4 / 0.363014e6 * c(N-3)) 48/(59)*(0.9258282831623875e16 / 0.7669235228057664e16 * c(N-2) + 0.3481e4 / 0.3264e4 * c(N) + 0.228389721191751e15 / 0.1278205871342944e16 * c(N-1) + 0.8673e4 / 0.1452056e7 * c(N-3)) 48/(59)*(-0.6025413881e10 / 0.21126554976e11 * c(N-2) - 0.59e2 / 0.68e2 * c(N) - 0.537416663e9 / 0.7042184992e10 * c(N-1));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
61 48/(17)*(-c(N-3) / 0.392e3 + c(N-2) / 0.784e3 + c(N-1) / 0.784e3) 48/(17)*(c(N-3) / 0.49e2 + 0.49579087e8 / 0.10149031312e11 * c(N-2) - 0.256702175e9 / 0.10149031312e11 * c(N-1)) 48/(17)*(-0.1244724001e10 / 0.21126554976e11 * c(N-2) + 0.3e1 / 0.68e2 * c(N) + 0.752806667e9 / 0.21126554976e11 * c(N-1)) 48/(17)*(-0.59e2 / 0.3136e4 * c(N-3) - 0.13249937023e11 / 0.48148892736e11 * c(N-1) + 0.2e1 / 0.17e2 * c(N) + 0.2083938599e10 / 0.8024815456e10 * c(N-2)) 48/(17)*(-0.6025413881e10 / 0.21126554976e11 * c(N-2) - 0.59e2 / 0.68e2 * c(N) - 0.537416663e9 / 0.7042184992e10 * c(N-1)) 48/(17)*(0.3e1 / 0.3136e4 * c(N-3) + 0.27010400129e11 / 0.345067064608e12 * c(N-2) + 0.234566387291e12 / 0.690134129216e12 * c(N-1) + 0.12e2 / 0.17e2 * c(N))];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
64
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
65 R = zeros(M,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
66 R(1:24) = reshape(U(1:4,:)',24,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
67 R(25:30) = U(5,:);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
68 R(31) = -c(5+1) / 0.6e1 + c(5) / 0.8e1 + c(5+2) / 0.8e1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
69 R(32:37) = U(6,:);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
70 R(38:39) = [-c(6-1) / 0.6e1 - c(6+2) / 0.6e1 - c(6) / 0.2e1 - c(6+1) / 0.2e1;...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
71 -c(6+1) / 0.6e1 + c(6) / 0.8e1 + c(6+2) / 0.8e1];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
72
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
73 R(M-38:M-37) = [-c(N-6) / 0.6e1 + c(N-7) / 0.8e1 + c(N-5) / 0.8e1;...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
74 -c(N-7) / 0.6e1 - c(N-4) / 0.6e1 - c(N-6) / 0.2e1 - c(N-5) / 0.2e1];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
75 R(M-36:M-31) = L(1,:);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
76 R(M-30) = -c(N-5) / 0.6e1 + c(N-6) / 0.8e1 + c(N-4) / 0.8e1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
77 R(M-29:M-24) = L(2,:);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
78 R(M-23:M) = reshape(L(3:6,:)',24,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
79
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
80 for i=7:N-6
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
81 R(40+(i-7)*5:44+(i-7)*5) = [-c(i-1) / 0.6e1 + c(i-2) / 0.8e1 + c(i) / 0.8e1,...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
82 -c(i-2) / 0.6e1 - c(i+1) / 0.6e1 - c(i-1) / 0.2e1 - c(i) / 0.2e1,...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
83 c(i-2) / 0.24e2 + 0.5e1 / 0.6e1 * c(i-1) + 0.5e1 / 0.6e1 * c(i+1) + c(i+2) / 0.24e2 + 0.3e1 / 0.4e1 * c(i),...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
84 -c(i-1) / 0.6e1 - c(i+2) / 0.6e1 - c(i) / 0.2e1 - c(i+1) / 0.2e1,...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
85 -c(i+1) / 0.6e1 + c(i) / 0.8e1 + c(i+2) / 0.8e1];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
86 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
87
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
88 R = R/h/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
89 D2 = -R;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
90 D2(1:4) = -48/17/h/h*[c(1)*(-11/6);c(1)*3;c(1)*(-3/2);c(1)*1/3] + D2(1:4);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
91 D2(M-3:M) = -48/17/h/h*[c(N)*1/3;c(N)*(-3/2);c(N)*3;c(N)*(-11/6)] + D2(M-3:M);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
92
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
93
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
94
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
95 BS = sparse(N,N);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96 BS(1,1:4) = -c(1)*1/h*[(-11/6);3;(-3/2);1/3];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
97 BS(N,N-3:N) = c(N)*1/h*[(-1/3);3/2;(-3);11/6];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
98 BS = sparse(BS);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
99
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
100 % %%Row and column indices%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
101 M = 78+(N-12)*5;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
102 rows = [kron([1;2;3;4],ones(6,1));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
103 5*ones(7,1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
104 6*ones(8,1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
105 kron((7:N-6)',ones(5,1));...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
106 (N-5)*ones(8,1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
107 (N-4)*ones(7,1);...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
108 kron([N-3;N-2;N-1;N],ones(6,1))];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
109
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
110 cols = zeros(M,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
111 cols(1:24) = kron(ones(4,1),[1;2;3;4;5;6]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
112 cols(25:39) = [(1:7)';(1:8)'];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
113 cols(M-23:M) = kron(ones(4,1),[N-5;N-4;N-3;N-2;N-1;N]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
114 cols(M-38:M-24) = [(N-7:N)';(N-6:N)'];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
115 for i=7:N-6
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
116 cols(40+(i-7)*5:44+(i-7)*5) = [i-2;i-1;i;i+1;i+2];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
117 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
118 D2 = sparse(rows,cols,D2);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
119 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
120 D2 = @D2_fun;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
121 end