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annotate +sbp/+implementations/d4_compatible_6.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents b19e142fcae1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
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Martin Almquist <martin.almquist@it.uu.se>
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1 function [H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m,...
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2 S3_1, S3_m, S_1, S_m] = d4_compatible_6(m,h)
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3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4 %%% 4:de ordn. SBP Finita differens %%%
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5 %%% operatorer framtagna av Ken Mattsson %%%
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6 %%% %%%
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7 %%% 6 randpunkter, diagonal norm %%%
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8 %%% %%%
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9 %%% Datum: 2013-11-11 %%%
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10 %%% %%%
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11 %%% %%%
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12 %%% H (Normen) %%%
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13 %%% D1 (approx f?rsta derivatan) %%%
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14 %%% D2 (approx andra derivatan) %%%
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15 %%% D3 (approx tredje derivatan) %%%
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16 %%% D2 (approx fj?rde derivatan) %%%
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17 %%% %%%
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18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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19
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20 % M?ste ange antal punkter (m) och stegl?ngd (h)
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21 % Notera att dessa opetratorer ?r framtagna f?r att anv?ndas n?r
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22 % vi har 3de och 4de derivator i v?r PDE
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23 % I annat fall anv?nd de "traditionella" som har noggrannare
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24 % randsplutningar f?r D1 och D2
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25
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26 % Vi b?rjar med normen. Notera att alla SBP operatorer delar samma norm,
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27 % vilket ?r n?dv?ndigt f?r stabilitet
326
b19e142fcae1 Fixed bug in setting of boundary derivative.
Jonatan Werpers <jonatan@werpers.com>
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28
266
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29 BP = 8;
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30 if(m<2*BP)
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31 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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32 end
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33
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34 H=speye(m,m);
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35 H_U=[0.7493827e7 / 0.25401600e8 0 0 0 0 0 0 0; 0 0.5534051e7 / 0.3628800e7 0 0 0 0 0 0; 0 0 0.104561e6 / 0.403200e6 0 0 0 0 0; 0 0 0 0.260503e6 / 0.145152e6 0 0 0 0; 0 0 0 0 0.43237e5 / 0.103680e6 0 0 0; 0 0 0 0 0 0.514081e6 / 0.403200e6 0 0; 0 0 0 0 0 0 0.3356179e7 / 0.3628800e7 0; 0 0 0 0 0 0 0 0.25631027e8 / 0.25401600e8;];
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36
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37 H(1:8,1:8)=H_U;
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38 H(m-7:m,m-7:m)=rot90(H_U,2);
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39 H=H*h;
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40 HI=inv(H);
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41
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42
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43 % First derivative SBP operator, 3rd order accurate at first 8 boundary points
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44
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45 q3=1/60;q2=-3/20;q1=3/4;
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46 % Q=q3*(diag(ones(m-3,1),3) - diag(ones(m-3,1),-3))+q2*(diag(ones(m-2,1),2) - diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
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47 stencil = [-q3,-q2,-q1,0,q1,q2,q3];
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48 d = (length(stencil)-1)/2;
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49 diags = -d:d;
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50 Q = stripeMatrix(stencil, diags, m);
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51
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52 Q_U = [0 0.26431903e8 / 0.43545600e8 0.39791489e8 / 0.152409600e9 -0.12747751e8 / 0.16934400e8 0.76099447e8 / 0.152409600e9 -0.1397443e7 / 0.12192768e8 0 0; -0.26431903e8 / 0.43545600e8 0 -0.13847476213e11 / 0.19559232000e11 0.35844843977e11 / 0.11735539200e11 -0.63413503537e11 / 0.23471078400e11 0.4764412871e10 / 0.3911846400e10 -0.1668252557e10 / 0.5867769600e10 0.842644697e9 / 0.29338848000e11; -0.39791489e8 / 0.152409600e9 0.13847476213e11 / 0.19559232000e11 0 -0.73834802771e11 / 0.23471078400e11 0.1802732209e10 / 0.325987200e9 -0.65514173e8 / 0.16299360e8 0.79341409141e11 / 0.58677696000e11 -0.1282384321e10 / 0.7823692800e10; 0.12747751e8 / 0.16934400e8 -0.35844843977e11 / 0.11735539200e11 0.73834802771e11 / 0.23471078400e11 0 -0.5274106087e10 / 0.1173553920e10 0.33743985841e11 / 0.5867769600e10 -0.6482602549e10 / 0.2607897600e10 0.1506017269e10 / 0.3911846400e10; -0.76099447e8 / 0.152409600e9 0.63413503537e11 / 0.23471078400e11 -0.1802732209e10 / 0.325987200e9 0.5274106087e10 / 0.1173553920e10 0 -0.7165829063e10 / 0.2607897600e10 0.23903110999e11 / 0.11735539200e11 -0.5346675911e10 / 0.11735539200e11; 0.1397443e7 / 0.12192768e8 -0.4764412871e10 / 0.3911846400e10 0.65514173e8 / 0.16299360e8 -0.33743985841e11 / 0.5867769600e10 0.7165829063e10 / 0.2607897600e10 0 -0.1060918223e10 / 0.11735539200e11 0.628353989e9 / 0.3911846400e10; 0 0.1668252557e10 / 0.5867769600e10 -0.79341409141e11 / 0.58677696000e11 0.6482602549e10 / 0.2607897600e10 -0.23903110999e11 / 0.11735539200e11 0.1060918223e10 / 0.11735539200e11 0 0.25889988599e11 / 0.39118464000e11; 0 -0.842644697e9 / 0.29338848000e11 0.1282384321e10 / 0.7823692800e10 -0.1506017269e10 / 0.3911846400e10 0.5346675911e10 / 0.11735539200e11 -0.628353989e9 / 0.3911846400e10 -0.25889988599e11 / 0.39118464000e11 0;];
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53
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54 Q(1:8,1:8)=Q_U;
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55 Q(m-7:m,m-7:m)=rot90( -Q_U ,2 );
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56
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57 e_1=sparse(m,1);e_1(1)=1;
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58 e_m=sparse(m,1);e_m(m)=1;
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59
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61 D1=H\(Q-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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62
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63 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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64
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65
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66
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67 % Second derivative, 1st order accurate at first 6 boundary points
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68 % m3=-1/90;m2=3/20;m1=-3/2;m0=49/18;
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69 %
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70 % M=m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
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71 % M_U=[0.4347276223e10 / 0.3736212480e10 -0.1534657609e10 / 0.1210809600e10 0.68879e5 / 0.3057600e7 0.1092927401e10 / 0.13076743680e11 0.18145423e8 / 0.968647680e9 -0.1143817e7 / 0.60540480e8 -0.355447739e9 / 0.65383718400e11 0.56081e5 / 0.16473600e8; -0.1534657609e10 / 0.1210809600e10 0.42416226217e11 / 0.18681062400e11 -0.228654119e9 / 0.345945600e9 -0.12245627e8 / 0.34594560e8 -0.2995295e7 / 0.46702656e8 0.52836503e8 / 0.691891200e9 0.119351e6 / 0.12812800e8 -0.634102039e9 / 0.65383718400e11; 0.68879e5 / 0.3057600e7 -0.228654119e9 / 0.345945600e9 0.5399287e7 / 0.4193280e7 -0.24739409e8 / 0.34594560e8 0.7878737e7 / 0.69189120e8 -0.1917829e7 / 0.31449600e8 0.39727e5 / 0.3660800e7 0.10259e5 / 0.4656960e7; 0.1092927401e10 / 0.13076743680e11 -0.12245627e8 / 0.34594560e8 -0.24739409e8 / 0.34594560e8 0.7780367599e10 / 0.3736212480e10 -0.70085363e8 / 0.69189120e8 -0.500209e6 / 0.6289920e7 -0.311543e6 / 0.17962560e8 0.278191e6 / 0.21525504e8; 0.18145423e8 / 0.968647680e9 -0.2995295e7 / 0.46702656e8 0.7878737e7 / 0.69189120e8 -0.70085363e8 / 0.69189120e8 0.7116321131e10 / 0.3736212480e10 -0.545081e6 / 0.532224e6 0.811631e6 / 0.11531520e8 -0.84101639e8 / 0.13076743680e11; -0.1143817e7 / 0.60540480e8 0.52836503e8 / 0.691891200e9 -0.1917829e7 / 0.31449600e8 -0.500209e6 / 0.6289920e7 -0.545081e6 / 0.532224e6 0.324760747e9 / 0.138378240e9 -0.65995697e8 / 0.49420800e8 0.1469203e7 / 0.13759200e8; -0.355447739e9 / 0.65383718400e11 0.119351e6 / 0.12812800e8 0.39727e5 / 0.3660800e7 -0.311543e6 / 0.17962560e8 0.811631e6 / 0.11531520e8 -0.65995697e8 / 0.49420800e8 0.48284442317e11 / 0.18681062400e11 -0.1762877569e10 / 0.1210809600e10; 0.56081e5 / 0.16473600e8 -0.634102039e9 / 0.65383718400e11 0.10259e5 / 0.4656960e7 0.278191e6 / 0.21525504e8 -0.84101639e8 / 0.13076743680e11 0.1469203e7 / 0.13759200e8 -0.1762877569e10 / 0.1210809600e10 0.10117212851e11 / 0.3736212480e10;];
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72 %
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73 % M(1:8,1:8)=M_U;
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74 %
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75 % M(m-7:m,m-7:m)=flipud( fliplr( M_U ) );
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76 % M=M/h;
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77
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78 S_U=[-0.12700800e8 / 0.7493827e7 0.185023321e9 / 0.89925924e8 0.39791489e8 / 0.44962962e8 -0.38243253e8 / 0.14987654e8 0.76099447e8 / 0.44962962e8 -0.34936075e8 / 0.89925924e8;]/h;
267
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79 S_1=sparse(1,m);
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80 S_1(1:6)=S_U;
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81 S_m=sparse(1,m);
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82
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83 S_m(m-5:m)=fliplr(-S_U);
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84
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85 %D2=H\(-M-e_1*S_1+e_m*S_m);
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86
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87
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88 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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89
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
90
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
91
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
92 % Third derivative, 1st order accurate at first 6 boundary points
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 % q4=7/240;q3=-3/10;q2=169/120;q1=-61/30;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
95 % Q3=q4*(diag(ones(m-4,1),4)-diag(ones(m-4,1),-4))+q3*(diag(ones(m-3,1),3)-diag(ones(m-3,1),-3))+q2*(diag(ones(m-2,1),2)-diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
97 % %QQ3=(-1/8*diag(ones(m-3,1),3) + 1*diag(ones(m-2,1),2) - 13/8*diag(ones(m-1,1),1) +13/8*diag(ones(m-1,1),-1) -1*diag(ones(m-2,1),-2) + 1/8*diag(ones(m-3,1),-3));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
98 %
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 % Q3_U = [0 -0.10882810591e11 / 0.5811886080e10 0.398713069e9 / 0.132088320e9 -0.1746657571e10 / 0.1162377216e10 0.56050639e8 / 0.145297152e9 -0.11473393e8 / 0.1162377216e10 -0.38062741e8 / 0.1452971520e10 0.30473e5 / 0.4392960e7; 0.10882810591e11 / 0.5811886080e10 0 -0.3720544343e10 / 0.830269440e9 0.767707019e9 / 0.207567360e9 -0.1047978301e10 / 0.830269440e9 0.1240729e7 / 0.14826240e8 0.6807397e7 / 0.55351296e8 -0.50022767e8 / 0.1452971520e10; -0.398713069e9 / 0.132088320e9 0.3720544343e10 / 0.830269440e9 0 -0.2870078009e10 / 0.830269440e9 0.74962049e8 / 0.29652480e8 -0.12944857e8 / 0.30750720e8 -0.17846623e8 / 0.103783680e9 0.68707591e8 / 0.1162377216e10; 0.1746657571e10 / 0.1162377216e10 -0.767707019e9 / 0.207567360e9 0.2870078009e10 / 0.830269440e9 0 -0.727867087e9 / 0.276756480e9 0.327603877e9 / 0.207567360e9 -0.175223717e9 / 0.830269440e9 0.1353613e7 / 0.726485760e9; -0.56050639e8 / 0.145297152e9 0.1047978301e10 / 0.830269440e9 -0.74962049e8 / 0.29652480e8 0.727867087e9 / 0.276756480e9 0 -0.1804641793e10 / 0.830269440e9 0.311038417e9 / 0.207567360e9 -0.1932566239e10 / 0.5811886080e10; 0.11473393e8 / 0.1162377216e10 -0.1240729e7 / 0.14826240e8 0.12944857e8 / 0.30750720e8 -0.327603877e9 / 0.207567360e9 0.1804641793e10 / 0.830269440e9 0 -0.1760949511e10 / 0.830269440e9 0.2105883973e10 / 0.1452971520e10; 0.38062741e8 / 0.1452971520e10 -0.6807397e7 / 0.55351296e8 0.17846623e8 / 0.103783680e9 0.175223717e9 / 0.830269440e9 -0.311038417e9 / 0.207567360e9 0.1760949511e10 / 0.830269440e9 0 -0.1081094773e10 / 0.528353280e9; -0.30473e5 / 0.4392960e7 0.50022767e8 / 0.1452971520e10 -0.68707591e8 / 0.1162377216e10 -0.1353613e7 / 0.726485760e9 0.1932566239e10 / 0.5811886080e10 -0.2105883973e10 / 0.1452971520e10 0.1081094773e10 / 0.528353280e9 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
101 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
102 % Q3(1:8,1:8)=Q3_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
103 % Q3(m-7:m,m-7:m)=flipud( fliplr( -Q3_U ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
104 % Q3=Q3/h^2;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
105 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
106 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
107 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
108 S2_U=[0.35e2 / 0.12e2 -0.26e2 / 0.3e1 0.19e2 / 0.2e1 -0.14e2 / 0.3e1 0.11e2 / 0.12e2;]/h^2;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
109 S2_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
110 S2_1(1:5)=S2_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
111 S2_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
112 S2_m(m-4:m)=fliplr(S2_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
113 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
114 %
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
115 %
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
116 % D3=H\(Q3 - e_1*S2_1 + e_m*S2_m +1/2*(S_1'*S_1) -1/2*(S_m'*S_m) ) ;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
117
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
118 % Fourth derivative, 0th order accurate at first 6 boundary points (still
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
119 % yield 4th order convergence if stable: for example u_tt=-u_xxxx
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
120
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
121 m4=7/240;m3=-2/5;m2=169/60;m1=-122/15;m0=91/8;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
122 % M4=m4*(diag(ones(m-4,1),4)+diag(ones(m-4,1),-4))+m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
123 stencil = [m4,m3,m2,m1,m0,m1,m2,m3,m4];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
124 d = (length(stencil)-1)/2;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
125 diags = -d:d;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
126 M4 = stripeMatrix(stencil, diags, m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
127
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
128
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
129 M4_U=[0.600485868980522851e18 / 0.274825314114120000e18 -0.1421010223681841e16 / 0.348984525859200e15 0.38908412970187e14 / 0.1586293299360000e16 0.10224077451922837e17 / 0.2243471951952000e16 -0.7577302712815639e16 / 0.1744922629296000e16 0.138091642084013e15 / 0.59351109840000e14 -0.3775041725375197e16 / 0.4486943903904000e16 0.9907210230881393e16 / 0.61072292025360000e17; -0.1421010223681841e16 / 0.348984525859200e15 0.3985852497808703e16 / 0.407903991264000e15 -0.90048788923861e14 / 0.15579666333000e14 -0.4312795866499e13 / 0.997098645312e12 0.4414634708891947e16 / 0.448694390390400e15 -0.886174803100459e15 / 0.99709864531200e14 0.4333e4 / 0.1000e4 -0.13800578064893047e17 / 0.15704303663664000e17; 0.38908412970187e14 / 0.1586293299360000e16 -0.90048788923861e14 / 0.15579666333000e14 0.2071682582321887e16 / 0.113306664240000e15 -0.769471337294003e15 / 0.41545776888000e14 0.112191585452033e15 / 0.166183107552000e15 0.7204491902193671e16 / 0.623186653320000e15 -0.24847093554379e14 / 0.3115933266600e13 0.943854037768721e15 / 0.545288321655000e15; 0.10224077451922837e17 / 0.2243471951952000e16 -0.4312795866499e13 / 0.997098645312e12 -0.769471337294003e15 / 0.41545776888000e14 0.3086874339649421e16 / 0.81580798252800e14 -0.396009005312111e15 / 0.16618310755200e14 0.348854811893087e15 / 0.249274661328000e15 0.895954627955053e15 / 0.224347195195200e15 -0.184881685054543e15 / 0.166183107552000e15; -0.7577302712815639e16 / 0.1744922629296000e16 0.4414634708891947e16 / 0.448694390390400e15 0.112191585452033e15 / 0.166183107552000e15 -0.396009005312111e15 / 0.16618310755200e14 0.3774861828677557e16 / 0.112173597597600e15 -0.5693689108983593e16 / 0.249274661328000e15 0.803944126167107e15 / 0.99709864531200e14 -0.19547569411550791e17 / 0.15704303663664000e17; 0.138091642084013e15 / 0.59351109840000e14 -0.886174803100459e15 / 0.99709864531200e14 0.7204491902193671e16 / 0.623186653320000e15 0.348854811893087e15 / 0.249274661328000e15 -0.5693689108983593e16 / 0.249274661328000e15 0.73965842628398389e17 / 0.2492746613280000e16 -0.2184472662036043e16 / 0.124637330664000e15 0.46667e5 / 0.10000e5; -0.3775041725375197e16 / 0.4486943903904000e16 0.4333e4 / 0.1000e4 -0.24847093554379e14 / 0.3115933266600e13 0.895954627955053e15 / 0.224347195195200e15 0.803944126167107e15 / 0.99709864531200e14 -0.2184472662036043e16 / 0.124637330664000e15 0.37593640125444199e17 / 0.2243471951952000e16 -0.37e2 / 0.4e1; 0.9907210230881393e16 / 0.61072292025360000e17 -0.13800578064893047e17 / 0.15704303663664000e17 0.943854037768721e15 / 0.545288321655000e15 -0.184881685054543e15 / 0.166183107552000e15 -0.19547569411550791e17 / 0.15704303663664000e17 0.46667e5 / 0.10000e5 -0.37e2 / 0.4e1 0.12766926490502478779e20 / 0.1099301256456480000e19;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
130
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
131 M4(1:8,1:8)=M4_U;
6009f2712d13 Moved and renamned all implementations.
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parents:
diff changeset
132
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
133 M4(m-7:m,m-7:m)=rot90( M4_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 M4=M4/h^3;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 S3_U=[-0.5e1 / 0.2e1 9 -12 7 -0.3e1 / 0.2e1;]/h^3;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
137 S3_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 S3_1(1:5)=S3_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
139 S3_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 S3_m(m-4:m)=fliplr(-S3_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
142 D4=H\(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 S_1 = S_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 S_m = S_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 S2_1 = S2_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 S2_m = S2_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 S3_1 = S3_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 S3_m = S3_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 % L=h*(m-1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 % x1=linspace(0,L,m)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 % x2=x1.^2/fac(2);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 % x3=x1.^3/fac(3);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 % x4=x1.^4/fac(4);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 % x5=x1.^5/fac(5);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 % x0=x1.^0/fac(1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 end