Forward Euler solution plotting

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Michael Swanson
Michael Swanson 2019-1-12
编辑： Torsten 2019-1-14
Hi,
I am trying to solve the differential equation dx/dy=x-y from x=0 to 1.5 using the forward euler method with step sizes 0.25, 0.05, and 0.01. I want to plot the approximations of all three step sizes on one plot, with the exact solution y=(x+1)-(1/3)e^x as well. I have the first approximation and plot with step size 0.25 in the code below. I was thinking I would use an array of step sizes where h=[0.25 0.05 0.01] and N=[6 30 150] but it's not working. How should I go about this?
h=0.25; % step size
N=6; % number of steps
y(1)=2/3; % Initial condition
for n=1:N
x(n+1)=n*h
y(n+1)= y(n)+h*(y(n)-x(n)) % FWD Euler solved for y(n+1)
end
plot(x,y)

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回答（1 个）

Torsten
Torsten 2019-1-14
编辑：Torsten 2019-1-14
function main
x0 = 0.0;
x1 = 1.5;
fun = @(x,y) y-x;
h = [0.25 0.05 0.01];
for i = 1:numel(h)
[x{i},y{i}] = euler(fun,x0,x1,h(i));
end
plot(x{1},y{1},x{2},y{2},x{3},y{3})
end
function [x,y] = euler(fun,x0,x1,h)
x(1) = x0;
y(1) = 2.0/3.0;
N = (x1-x0)/h;
for i=2:N+1
y(i) = y(i-1) + h*fun(x(i-1),y(i-1));
x(i) = x(i-1) + h;
end
end

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