function [w, yA, MH, K, F, lambda] = ParabolikGeriFark(L,T,m,n,alpha) % u_t - alpha^2 u_xx = 0, u(0,t) = fx0 % u(L,t) = fxL, u(x,0) = ft0 fx0 = @(x,t) 0; fxL = @(x,t) 0; ft0 = @(x,t) 2*sin(2*pi*x); h = L/m; k = T/n; x = 0:h:L; t = 0:k:T; lambda = (alpha^2)*k/(h^2); mu = (1+2*lambda); %BC'S for j = 1:n+1 w(1,j) = fx0(x(1),t(j)); w(m+1,j) = fxL(x(m+1),t(j)); end % IC for i = 1:m+1 w(i,1) = ft0(x(i),t(1)); end % KATSAYILAR MATRİSİ for i = 1:m-1 K(i,i) = mu; end for i = 1:m-2 K(i,i+1) = -lambda; K(i+1,i) = -lambda; end % Denklem sistemi çözümü for j = 2:n+1 F(1,1) = w(2,j-1) + lambda*w(1,j); F(m-1,1) = w(m,j-1) + lambda*w(m+1,j); for i = 2:m-2 F(i,1) = w(i+1,j-1); end ww = K\F; for i = 2:m w(i,j) = ww(i-1,1); end end % Analitik çözüm [TT,XX] = meshgrid(t,x); yA = 2*exp(-((pi^2)/4)*TT).*sin(2*pi*XX); MH = abs(yA - w);