我试图在我的 matlab 代码序列中实现拉普拉斯方程，如下所示。我创建了这个 LaplaceExplicit.m 并因此使用了另一个函数 numgrid 。但是，它显示错误为“输入变量 n 未定义”。应该做什么？代码如下 -
function [x,y,T]= LaplaceExplicit(n,m,Dx,Dy)
echo off;
numgrid(n,m);
R = 5.0;
T = R*ones(n+1,m+1); % All T(i,j) = 1 includes all boundary conditions
x = [0:Dx:n*Dx];y=[0:Dy:m*Dy]; % x and y vectors
for i = 1:n % Boundary conditions at j = m+1 and j = 1
6
T(i,m+1) = T(i,m+1)+ R*x(i)*(1-x(i));
T(i,1) = T(i,1) + R*x(i)*(x(i)-1);
end;
TN = T; % TN = new iteration for solution
err = TN-T;
% Parameters in the solution
beta = Dx/Dy;
denom = 2*(1+beta^2);
% Iterative procedure
epsilon = 1e-5; % tolerance for convergence
imax = 1000; % maximum number of iterations allowed
k = 1; % initial index value for iteration
% Calculation loop
while k<= imax
for i = 2:n
for j = 2:m
TN(i,j)=(T(i-1,j)+T(i+1,j)+beta^2*(T(i,j-1)+T(i,j+1)))/denom;
err(i,j) = abs(TN(i,j)-T(i,j));
end;
end;
T = TN; k = k + 1;
errmax = max(max(err));
if errmax < epsilon
[X,Y] = meshgrid(x,y);
figure(2);contour(X,Y,T',20);xlabel('x');ylabel('y');
title('Laplace equation solution - Dirichlet boundary conditions Explicit');
figure(3);surfc(X,Y,T');xlabel('x');ylabel('y');zlabel('T(x,y)');
title('Laplace equation solution - Dirichlet boundary conditions Explicit');
fprintf('Convergence achieved after %i iterations.\n',k);
fprintf('See the following figures:\n');
fprintf('==========================\n');
fprintf('Figure 1 - sketch of computational grid \n');
fprintf('Figure 2 - contour plot of temperature \n');
fprintf('Figure 3 - surface plot of temperature \n');
return
end;
end;
fprintf('\n No convergence after %i iterations.',k);