Euler method doesn't give correct output-CodePudding

I'm trying to write a MATLAB code for the Forward Euler method, but I don't think the output is completely correct.

This is my code:

function [tHist ,uHist] = ForwardEuler(f,tspan ,u0,nsteps)

T = [tspan(1) :nsteps: tspan(2)];
u = zeros(1,nsteps);
u(n) = u0;
h = (tspan(2) - tspan(1))/nsteps;
for i= 1: nsteps 
    u(i 1) = u(i)   h*f(T(i),u(i));
    tHist = [u(i 1)*T(i)];
    uHist = [u(i 1)];
end
end

CodePudding user response：

A minimal straightforward implementation could look like

function [tHist ,uHist] = ForwardEuler(f,tspan ,u0,nsteps)
    tHist = linspace(tspan(1), tspan(2), nsteps 1);
    h = tHist(2)-tHist(1);
    uHist = zeros(nsteps 1,length(u0));
    uHist(1,:)=u0;
    for i = 1:nsteps
        uHist(i 1,:) = uHist(i,:)   h*f(tHist(i),uHist(i,:));
    end%for
end%function

Test the routine with the circle equation

[T,U] = ForwardEuler(@(t,u)[u(2), -u(1)], [0,6.5], [1,0], 60);
plot(U(:,1),U(:,2));

which produces the expected outward spiral.