Question about Forward time center space 1D matlab code

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Murad Alzahrani 2020-6-9

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评论： darova 2020-6-12

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Hi. I tried make code I can solve this problem in Forward time center space 1D:

As you see, but my code naver show me completely linea when plot the steady state temperature.

Code:

    clear variables
    close all
    %1 Function parameters
    N  = 10;
    Lx = 1;
    dx = Lx/(N-1);
    x  = 0:dx:Lx;
    alpha = 0.5;   % To insure stability alpha = dt/dx^2 < = 1/2
    % 2. Time vector
    M = 100;
    tf = 100;     
    dt = tf/(M-1);
    t = 0:dt:tf;
    % 4. Initial and boundary conditions
    f  = @(x) x;   % initial cond. f(x)
    g1 = @(t) 100;     % boundary conditions g1(t) and g2(t)
    g2 = @(t) 0;
    % 5. Inilization of the heat equation
    u      =  zeros(N,M);
    u(:,1) =  f(x);
    u(1,:) =  g1(t);
    % 6. Implementation of the explicit method
    for j= 1:M-1       % Time Loop 
         for i= 2:N-1  % Space Loop
           u(i,j+1) = alpha*(u(i-1,j))+(1-2*alpha)*u(i,j) + alpha*u(i+1,j);
         end
         % Vectorize the inner for loop with this line to gain some speed.
         % u(2:N-1,j+1) = alpha*(u(1:N-2,j))+(1-2*alpha)*u(2:N-1,j) + alpha*u(3:N,j);
     % Insert boundary conditions for i = 1 and i = N here.
     u(2,j+1) =  alpha*u(1,j) + (1-2*alpha)*u(2,j) + alpha*u(3,j);
     u(N,j+1) =  2*alpha*u(N-1,j)+(1-2*alpha)*u(N,j)+ 2*alpha*dx*g2(t);
    end
    % Plot results
    figure
    plot(x,u(1:end,1:30),'linewidth',2);
    a = ylabel('Temperature');
    set(a,'Fontsize',14);
    a = xlabel('x');
    set(a,'Fontsize',14);
    a=title(['Using The Explicit Method - alpha =' num2str(alpha)]);
    legend('Explicit soln')
    set(a,'Fontsize',16);
    xlim([0 1]);
    grid;
    figure