1D Transient Diffusion (MATLAB code)

clear; clc;% clear the screen and memory

Nx=500; %number of space nodes

Nt=10000; %number of time nodes

Lx=0.3; %length of space (m)

Lt=10; %length of physical time (s)

dx=Lx/(Nx-1); %grid spacing

dt=Lt/(Nt-1); %time step

c=0.000097; %speed of wave (constant)

a=c*dt/dx.^2;

u=100*ones(Nx,1); %initialization of matrix for the property under investigation

x=zeros(Nx,1); %initialization of space

for i=1:Nx-1 %space loop

    x(i+1)=x(i)+dx;

end

u(1)=-20; %boundary condition

u(Nx)=50; %boundary condition

for t=0:dt:Lt %time loop

    un=u; %u(i,t)

    for i=2:Nx-1 %solution loop, backward in space forward in time

        u(i)=((1-2*a)*un(i))+a*(un(i+1)+un(i-1)); %discretized equation, u(i,t+1)

    end

    plot(x,u) %plotting

    title({t;'Time Elaplsed (s)'},'FontSize',38.5);

    pause(0.001)

end