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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 13 Oct 2016 09:34:42 +0200
parents f7ac3cd6eeaa
children 43d02533bea3
comparison
equal deleted inserted replaced
302:f39f98b59f61 303:f18142c1530b
1 function [H, HI, D1, D2, e_l, e_r, d_l, d_r] = d2_variable_4(m,h) 1 function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_4(m,h)
2 2
3 BP = 4; 3 BP = 4;
4 if(m<2*BP) 4 if(m<2*BP)
5 error(['Operator requires at least ' num2str(2*BP) ' grid points']); 5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
6 end 6 end
7 7
8 N = m;
9
10 H = spspeye(N);
11 H(1,1) = 17/48; H(2,2) = 59/48; H(3,3) = 43/48; H(4,4) = 49/48;
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;
13 H = h*H;
14
15 HI = inv(H);
16
17 H = sparse(H);
18 HI = sparse(HI);
19 8
20 9
21 S = sparse(N,N);
22 S(1,1:4) = 1/h*[(-11/6);3;(-3/2);1/3];
23 S(N,N-3:N) = 1/h*[(-1/3);3/2;(-3);11/6];
24 S = sparse(S);
25 10
11 % Norm
12 Hv = ones(m,1);
13 Hv(1:4) = [17/48 59/48 43/48 49/48];
14 Hv(m-3:m) = rot90(Hv(1:4),2);
15 Hv = h*Hv;
16 H = spdiag(Hv, 0);
17 HI = spdiag(1./Hv, 0);
18
19
20 % Boundary operators
26 e_l = sparse(m,1); 21 e_l = sparse(m,1);
27 e_l(1) = 1; 22 e_l(1) = 1;
23 e_r = rot90(e_l, 2);
28 24
29 e_r = sparse(m,1); 25 d1_l = sparse(m,1);
30 e_r(end) = 1; 26 d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
27 d1_r = -rot90(d1_l, 2);
31 28
32 d_l = S(1,:)';
33 d_r = S(end,:)';
34 29
35 e=ones(m,1);
36 Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12;
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;];
38 Q(1:4,1:4)=Q_U;
39 Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
40 30
41 D1=HI*(Q-1/2*(e_l*e_l')+1/2*(e_r*e_r')) ;
42 31
32 S = d1_l*d1_l' + d1_r*d1_r';
33
34 stencil = [1/12 -2/3 0 2/3 -1/12];
35 diags = -2:2;
36
37 Q_U = [
38 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
39 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
40 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
41 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
42 ];
43
44 Q = stripeMatrix(stencil, diags, m);
45 Q(1:4,1:4) = Q_U;
46 Q(m-3:m,m-3:m) = -rot90(Q_U, 2);
47
48 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
49
50
51 N = m;
43 function D2 = D2_fun(c) 52 function D2 = D2_fun(c)
44 M = 78+(N-12)*5; 53 M = 78+(N-12)*5;
45 %h = 1/(N-1); 54 %h = 1/(N-1);
46 55
47 56
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);... 57 U = [
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));... 58 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);...
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));... 59 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));...
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);... 60 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));...
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;... 61 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);...
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)]; 62 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;...
63 -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)
64 ];
54 65
55 66
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;... 67 L = [
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);... 68 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;...
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));... 69 -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);...
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));... 70 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));...
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));... 71 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));...
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))]; 72 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));...
73 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))
74 ];
62 75
63 76
64 77
65 R = sparse(M,1); 78 R = sparse(M,1);
66 R(1:24) = reshape(U(1:4,:)',24,1); 79 R(1:24) = reshape(U(1:4,:)',24,1);
67 R(25:30) = U(5,:); 80 R(25:30) = U(5,:);
68 R(31) = -c(5+1) / 0.6e1 + c(5) / 0.8e1 + c(5+2) / 0.8e1; 81 R(31) = -c(5+1)/0.6e1 + c(5)/0.8e1 + c(5+2)/0.8e1;
69 R(32:37) = U(6,:); 82 R(32:37) = U(6,:);
70 R(38:39) = [-c(6-1) / 0.6e1 - c(6+2) / 0.6e1 - c(6) / 0.2e1 - c(6+1) / 0.2e1;... 83 R(38:39) = [-c(6-1)/0.6e1 - c(6+2)/0.6e1 - c(6)/0.2e1 - c(6+1)/0.2e1;...
71 -c(6+1) / 0.6e1 + c(6) / 0.8e1 + c(6+2) / 0.8e1]; 84 -c(6+1)/0.6e1 + c(6)/0.8e1 + c(6+2)/0.8e1];
72 85
73 R(M-38:M-37) = [-c(N-6) / 0.6e1 + c(N-7) / 0.8e1 + c(N-5) / 0.8e1;... 86 R(M-38:M-37) = [-c(N-6)/0.6e1 + c(N-7)/0.8e1 + c(N-5)/0.8e1;...
74 -c(N-7) / 0.6e1 - c(N-4) / 0.6e1 - c(N-6) / 0.2e1 - c(N-5) / 0.2e1]; 87 -c(N-7)/0.6e1 - c(N-4)/0.6e1 - c(N-6)/0.2e1 - c(N-5)/0.2e1];
75 R(M-36:M-31) = L(1,:); 88 R(M-36:M-31) = L(1,:);
76 R(M-30) = -c(N-5) / 0.6e1 + c(N-6) / 0.8e1 + c(N-4) / 0.8e1; 89 R(M-30) = -c(N-5)/0.6e1 + c(N-6)/0.8e1 + c(N-4)/0.8e1;
77 R(M-29:M-24) = L(2,:); 90 R(M-29:M-24) = L(2,:);
78 R(M-23:M) = reshape(L(3:6,:)',24,1); 91 R(M-23:M) = reshape(L(3:6,:)',24,1);
79 92
80 for i=7:N-6 93 for i=7:N-6
81 R(40+(i-7)*5:44+(i-7)*5) = [-c(i-1) / 0.6e1 + c(i-2) / 0.8e1 + c(i) / 0.8e1,... 94 R(40+(i-7)*5:44+(i-7)*5) = [
82 -c(i-2) / 0.6e1 - c(i+1) / 0.6e1 - c(i-1) / 0.2e1 - c(i) / 0.2e1,... 95 -c(i-1)/0.6e1 + c(i-2)/0.8e1 + c(i)/0.8e1,...
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),... 96 -c(i-2)/0.6e1 - c(i+1)/0.6e1 - c(i-1)/0.2e1 - c(i)/0.2e1,...
84 -c(i-1) / 0.6e1 - c(i+2) / 0.6e1 - c(i) / 0.2e1 - c(i+1) / 0.2e1,... 97 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),...
85 -c(i+1) / 0.6e1 + c(i) / 0.8e1 + c(i+2) / 0.8e1]; 98 -c(i-1)/0.6e1 - c(i+2)/0.6e1 - c(i)/0.2e1 - c(i+1)/0.2e1,...
99 -c(i+1)/0.6e1 + c(i)/0.8e1 + c(i+2)/0.8e1
100 ];
86 end 101 end
87 102
88 R = R/h/h; 103 R = R/h/h;
89 D2 = -R; 104 D2 = -R;
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); 105 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);