octave:2> A=toeplitz([-4,1,0,0,0]) A = -4 1 0 0 0 1 -4 1 0 0 0 1 -4 1 0 0 0 1 -4 1 0 0 0 1 -4 octave:3> A=toeplitz([-4,1,0]) A = -4 1 0 1 -4 1 0 1 -4 octave:4> I=eye(3) I = 1 0 0 0 1 0 0 0 1 octave:5> kron(I,A) ans = -4 1 0 -0 0 0 -0 0 0 1 -4 1 0 -0 0 0 -0 0 0 1 -4 0 0 -0 0 0 -0 -0 0 0 -4 1 0 -0 0 0 0 -0 0 1 -4 1 0 -0 0 0 0 -0 0 1 -4 0 0 -0 -0 0 0 -0 0 0 -4 1 0 0 -0 0 0 -0 0 1 -4 1 0 0 -0 0 0 -0 0 1 -4 octave:6> Ax=d(1)*toeplitz([-2,1,0]) error: `d' undefined near line 6 column 4 error: evaluating binary operator `*' near line 6, column 8 error: evaluating assignment expression near line 6, column 3 octave:6> d(1)=2 d = 2 octave:7> Ax=d(1)*toeplitz([-2,1,0]) Ax = -4 2 0 2 -4 2 0 2 -4 octave:8> kron(I,Ax) ans = -4 2 0 -0 0 0 -0 0 0 2 -4 2 0 -0 0 0 -0 0 0 2 -4 0 0 -0 0 0 -0 -0 0 0 -4 2 0 -0 0 0 0 -0 0 2 -4 2 0 -0 0 0 0 -0 0 2 -4 0 0 -0 -0 0 0 -0 0 0 -4 2 0 0 -0 0 0 -0 0 2 -4 2 0 0 -0 0 0 -0 0 2 -4 octave:9> Ax=toeplitz([-2,1,0]) Ax = -2 1 0 1 -2 1 0 1 -2 octave:10> A=toeplitz([-2,1,0]) A = -2 1 0 1 -2 1 0 1 -2 octave:11> kron(I,Ax) ans = -2 1 0 -0 0 0 -0 0 0 1 -2 1 0 -0 0 0 -0 0 0 1 -2 0 0 -0 0 0 -0 -0 0 0 -2 1 0 -0 0 0 0 -0 0 1 -2 1 0 -0 0 0 0 -0 0 1 -2 0 0 -0 -0 0 0 -0 0 0 -2 1 0 0 -0 0 0 -0 0 1 -2 1 0 0 -0 0 0 -0 0 1 -2 octave:12> kron(I,A) ans = -2 1 0 -0 0 0 -0 0 0 1 -2 1 0 -0 0 0 -0 0 0 1 -2 0 0 -0 0 0 -0 -0 0 0 -2 1 0 -0 0 0 0 -0 0 1 -2 1 0 -0 0 0 0 -0 0 1 -2 0 0 -0 -0 0 0 -0 0 0 -2 1 0 0 -0 0 0 -0 0 1 -2 1 0 0 -0 0 0 -0 0 1 -2 octave:13> kron(A,I) ans = -2 -0 -0 1 0 0 0 0 0 -0 -2 -0 0 1 0 0 0 0 -0 -0 -2 0 0 1 0 0 0 1 0 0 -2 -0 -0 1 0 0 0 1 0 -0 -2 -0 0 1 0 0 0 1 -0 -0 -2 0 0 1 0 0 0 1 0 0 -2 -0 -0 0 0 0 0 1 0 -0 -2 -0 0 0 0 0 0 1 -0 -0 -2 octave:14> kron(I,A)+kron(A,I) ans = -4 1 0 1 0 0 0 0 0 1 -4 1 0 1 0 0 0 0 0 1 -4 0 0 1 0 0 0 1 0 0 -4 1 0 1 0 0 0 1 0 1 -4 1 0 1 0 0 0 1 0 1 -4 0 0 1 0 0 0 1 0 0 -4 1 0 0 0 0 0 1 0 1 -4 1 0 0 0 0 0 1 0 1 -4 octave:15> kron(I,A) ans = -2 1 0 -0 0 0 -0 0 0 1 -2 1 0 -0 0 0 -0 0 0 1 -2 0 0 -0 0 0 -0 -0 0 0 -2 1 0 -0 0 0 0 -0 0 1 -2 1 0 -0 0 0 0 -0 0 1 -2 0 0 -0 -0 0 0 -0 0 0 -2 1 0 0 -0 0 0 -0 0 1 -2 1 0 0 -0 0 0 -0 0 1 -2 octave:16> kron(A,I) ans = -2 -0 -0 1 0 0 0 0 0 -0 -2 -0 0 1 0 0 0 0 -0 -0 -2 0 0 1 0 0 0 1 0 0 -2 -0 -0 1 0 0 0 1 0 -0 -2 -0 0 1 0 0 0 1 -0 -0 -2 0 0 1 0 0 0 1 0 0 -2 -0 -0 0 0 0 0 1 0 -0 -2 -0 0 0 0 0 0 1 -0 -0 -2 octave:17> A=toeplitz([-2,1,0]) A = -2 1 0 1 -2 1 0 1 -2 octave:18> Axx=d(1)*toeplitz([-2,1,0])/h^2 error: `h' undefined near line 18 column 29 error: evaluating binary operator `^' near line 18, column 30 error: evaluating binary operator `/' near line 18, column 28 error: evaluating assignment expression near line 18, column 4 octave:18> h=1/2 h = 0.50000 octave:19> Axx=d(1)*toeplitz([-2,1,0])/h^2 Axx = -16 8 0 8 -16 8 0 8 -16 octave:20> Ax=-c(1)*toeplitz([0,-1,0],[0,1,0])/(2*h) error: `c' undefined near line 20 column 5 error: evaluating prefix operator `-' near line 20, column 4 error: evaluating binary operator `*' near line 20, column 9 error: evaluating binary operator `/' near line 20, column 36 error: evaluating assignment expression near line 20, column 3 octave:20> c(1)=1 c = 1 octave:21> Ax=-c(1)*toeplitz([0,-1,0],[0,1,0])/(2*h) Ax = -0 -1 -0 1 -0 -1 -0 1 -0 octave:22> Axx+Ax ans = -16 7 0 9 -16 7 0 9 -16 octave:23> kron(I,Axx+Ax) ans = -16 7 0 -0 0 0 -0 0 0 9 -16 7 0 -0 0 0 -0 0 0 9 -16 0 0 -0 0 0 -0 -0 0 0 -16 7 0 -0 0 0 0 -0 0 9 -16 7 0 -0 0 0 0 -0 0 9 -16 0 0 -0 -0 0 0 -0 0 0 -16 7 0 0 -0 0 0 -0 0 9 -16 7 0 0 -0 0 0 -0 0 9 -16 octave:24> Ayy=d(2)*toeplitz([-2,1,0])/h^2 error: invalid vector index = 2 error: evaluating binary operator `*' near line 24, column 9 error: evaluating binary operator `/' near line 24, column 28 error: evaluating assignment expression near line 24, column 4 octave:24> d(2)=3 d = 2 3 octave:25> Ayy=d(2)*toeplitz([-2,1,0])/h^2 Ayy = -24 12 0 12 -24 12 0 12 -24 octave:26> Ay=-c(2)*toeplitz([0,-1,0],[0,1,0])/(2*h) error: invalid vector index = 2 error: evaluating prefix operator `-' near line 26, column 4 error: evaluating binary operator `*' near line 26, column 9 error: evaluating binary operator `/' near line 26, column 36 error: evaluating assignment expression near line 26, column 3 octave:26> c(2)=-5 c = 1 -5 octave:27> Ay=-c(2)*toeplitz([0,-1,0],[0,1,0])/(2*h) Ay = 0 5 0 -5 0 5 0 -5 0 octave:28> Ayy+Ay ans = -24 17 0 7 -24 17 0 7 -24 octave:29> kron(Ayy+Ay,I) ans = -24 -0 -0 17 0 0 0 0 0 -0 -24 -0 0 17 0 0 0 0 -0 -0 -24 0 0 17 0 0 0 7 0 0 -24 -0 -0 17 0 0 0 7 0 -0 -24 -0 0 17 0 0 0 7 -0 -0 -24 0 0 17 0 0 0 7 0 0 -24 -0 -0 0 0 0 0 7 0 -0 -24 -0 0 0 0 0 0 7 -0 -0 -24 octave:30> kron(I,Axx+Ax)+kron(Ayy+Ay,I) ans = -40 7 0 17 0 0 0 0 0 9 -40 7 0 17 0 0 0 0 0 9 -40 0 0 17 0 0 0 7 0 0 -40 7 0 17 0 0 0 7 0 9 -40 7 0 17 0 0 0 7 0 9 -40 0 0 17 0 0 0 7 0 0 -40 7 0 0 0 0 0 7 0 9 -40 7 0 0 0 0 0 7 0 9 -40 octave:31> Axx+Ax ans = -16 7 0 9 -16 7 0 9 -16 octave:32> x=linspace(0,2,3) x = 0 1 2 octave:33> [X,Y]=meshgrid(x); octave:34> X X = 0 1 2 0 1 2 0 1 2 octave:35> Y Y = 0 0 0 1 1 1 2 2 2 octave:36> x=linspace(0,2,3) x = 0 1 2 octave:37> y=linspace(10,12,3) y = 10 11 12 octave:38> [X,Y]=meshgrid(x,y); octave:39> X X = 0 1 2 0 1 2 0 1 2 octave:40> Y Y = 10 10 10 11 11 11 12 12 12 octave:41> x=linspace(0,2,100); octave:42> y=linspace(10,12,100); octave:43> [X,Y]=meshgrid(x,y); octave:44> Z=X+Y.^2; octave:45> mesh(X,Y,Z) octave:46> Z=X+sin(Y); octave:47> mesh(X,Y,Z) octave:48> xlabel('x') octave:49> ylabel('y') octave:50> x=linspace(0,2*pi,10); octave:51> y=linspace(0,2*pi,10); octave:52> [X,Y]=meshgrid(x,y); octave:53> Z=X+sin(Y); octave:54> mesh(X,Y,Z) octave:55> xlabel('x') octave:56> ylabel('y') octave:57> Z Z = Columns 1 through 7: 0.00000 0.69813 1.39626 2.09440 2.79253 3.49066 4.18879 0.64279 1.34092 2.03905 2.73718 3.43531 4.13345 4.83158 0.98481 1.68294 2.38107 3.07920 3.77733 4.47547 5.17360 0.86603 1.56416 2.26229 2.96042 3.65855 4.35668 5.05482 0.34202 1.04015 1.73828 2.43642 3.13455 3.83268 4.53081 -0.34202 0.35611 1.05424 1.75237 2.45051 3.14864 3.84677 -0.86603 -0.16789 0.53024 1.22837 1.92650 2.62463 3.32276 -0.98481 -0.28668 0.41146 1.10959 1.80772 2.50585 3.20398 -0.64279 0.05534 0.75348 1.45161 2.14974 2.84787 3.54600 -0.00000 0.69813 1.39626 2.09440 2.79253 3.49066 4.18879 Columns 8 through 10: 4.88692 5.58505 6.28319 5.52971 6.22784 6.92597 5.87173 6.56986 7.26799 5.75295 6.45108 7.14921 5.22894 5.92707 6.62521 4.54490 5.24303 5.94117 4.02090 4.71903 5.41716 3.90211 4.60025 5.29838 4.24413 4.94227 5.64040 4.88692 5.58505 6.28319 octave:58> y=linspace(0,2,3); octave:59> x=linspace(0,2,3); octave:60> y=linspace(10,12,3); octave:61> [X,Y]=meshgrid(x,y); octave:62> X X = 0 1 2 0 1 2 0 1 2 octave:63> Y Y = 10 10 10 11 11 11 12 12 12 octave:64> A=[1,2,3;4,5,6;7,8,9] A = 1 2 3 4 5 6 7 8 9 octave:65> reshape(A,9,1) ans = 1 4 7 2 5 8 3 6 9 octave:66> reshape(A',9,1) ans = 1 2 3 4 5 6 7 8 9 octave:67> x=linspace(0,pi,25); octave:68> [X,Y]=meshgrid(x); octave:69> mesh(X,Y,(sin(X).*sin(Y)).^6) octave:70> contourf(X,Y,(sin(X).*sin(Y)).^6) octave:71> axis square octave:72> colorbar octave:73> caloredirichlet Press a key to continue... octave:74> octave:74> caloreneumann Press a key to continue... octave:75> octave:75> diary off