Thomas algorithm - tridiagonal matrix

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Cesar Cardenas 2023-3-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1921370-thomas-algorithm-tridiagonal-matrix

评论： Cesar Cardenas 2023-3-2

Is there any other way to code and solve the tridiagonal matrix? the idea would be to try to get the plot shown. Matlab beginner, so, no sure how to do it. Any help will be greatly appreciated. Thanks

clear
cm=1/100;
delta = 1*cm;
nu=1e-6;
Uinf=1;
H=2*delta;
y=linspace(0,H,40);
u=Uinf*erf(3*y/delta);
dy=mean(diff(y));
dx=100*dy;
Q=nu*dx/Uinf/dy^2;
a=-Q;
c=-Q;
b=1+2*Q;
N=length(y)-2;
M = diag(b*ones(1,N)) + diag(c*ones(1,N-1),1) + diag(a*ones(1,N-1),-1);
%Constant Ue
Ue = @(x) Uinf;
u = u(2:end-1);
x=0;
uall=[0,u,Ue(x)];

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采纳的回答

Torsten 2023-3-2

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1921370-thomas-algorithm-tridiagonal-matrix#answer_1183170

编辑：Torsten 2023-3-2

在 MATLAB Online 中打开

clear

cm=1/100;

delta = 1*cm;

nu=1e-6;

Uinf=1;

H=2*delta;

y=linspace(0,H,40);

u=Uinf*erf(3*y/delta);

dy=mean(diff(y));

dx=100*dy;

Q=nu*dx/Uinf/dy^2;

a=-Q;

c=-Q;

b=1+2*Q;

N = length(y);

M = diag(b*ones(1,N)) + diag(c*ones(1,N-1),1) + diag(a*ones(1,N-1),-1);

M(1,:) = [1,zeros(1,N-1)];

M(end,:) = [zeros(1,N-1),1];

%Constant Ue

Ue = @(x) Uinf;

u = u(2:end-1);

x=0;

uall=[0,u,Ue(x)];

sol = M\uall.';

plot(y,sol)

grid on

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Torsten 2023-3-2

You can assign values to certain elements in a matrix by using a loop. But if the above line to define M is correct, it's elegant, isn't it ? Why do you want to define it differently ?

Cesar Cardenas 2023-3-2