I have to solve 1d heat equation using ftcs with given boundry condition. u(0,t)=0, u(l,t)=0 u(x,0) = f(x) but i cannot understand how to use my this in for loop .

f(x)=100; %given value of function

h = 0.1;% given value of step size

k = 0.01;%given value of time-step size

alpha = 0.25; % given value of thermal diffusivity in heat equation

lambda = alpha*k/h^2; %Difference method parameter

l = 1 ; % legth of thin rod

t = 1 ; % final time

n = l/h ; % intervals at x-axis

% W - Matrix for generating solutions

W(0,t)=W(l,t) = 0 ; %Dirichlet boundry conditions

% imposition of boundry conditions

W =zeroes (length(x), length(t));

W(:,1)=f(x); %intial condition

W(1,:)=0.0; %condition at x = 0

W(end,:)=0.0; %condition at x = L

%genrating the matrix

x = (0:h:l);

t=(0:k:t)';

W = zeroes(length(x), Length(t));

for i = 0:0.1

for j = 0:0.001

W(i,j) = W((1-2*lambda)*ones(n-1,1),0) + (lambda*ones(n-2,1),1) ;

end

end

[Star Strider]

Consider using bvp4c.

.

Answer 1

[Sreedhar Arumugam]

It is my understanding that you want to implement a solution for 1-D heat solution using FTCS method.

Please refer to these submissions made on FileExchange -

https://www.mathworks.com/matlabcentral/fileexchange/54617-ftcs-heat-equation?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/fileexchange/53407-obtaining-the-steady-state-solution-of-the-1-d-heat-conduction-equations-using-ftcs-method?s_tid=srchtitle