Euler Method IVP Coding Help

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Bailey Smith
Bailey Smith 2018-7-30
回答： John 2023-8-5
I have an IVP problem I'm trying to solve with Euler's Method. The problem is: dy/dx = 1-x+1, y(0) = 1. My time step is 0.01 and my x final is 3. I get an "Index exceeds matrix dimensions." error when I try and run the code. Where am I going wrong? Here is my code:
clear; clc;
%inputs
xo=input('Enter x initial: ');
yo=input('Enter y initial: ');
dx=input('Enter delta x (time step): ');
xf=input('Enter x final: ');
x(1)=xo;
y(1)=yo;
n=1;
% function [out] = Euler(x,y)
% out=1-x+y;
% end
while x(n)<=xf
y(n+1)=y(n)+Euler(x(n),y(n))*(dx);
n=n+1;
end

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回答（2 个）

Aquatris
Aquatris 2018-7-30
Your x vector only has a single element in it. After while loop goes once, it tries to reach x(2), which does not exist. That is why you are getting index exceeds error.
John
John 2023-8-5
w0=0.5;
a=0;
b=2;
hh=[0.5 0.2 0.1 0.05 0.01 0.005 0.001];
f=@(t,y) y-t^2+1;
for j=1:7
we(1,j)=w0;
wm(1,j)=w0;
wr(1,j)=w0;
h=hh(j);
n=(b-a)/h;
for i=1:n
t=(i-1)*h;
we(i+1,j)=we(i,j)+h*f(t,we(i,j));
wm(i+1,j)=wm(i,j)+h*f(t+h/2,wm(i,j)+(h/2)*f(t,wm(i,j)));
k1=h*f(t,wr(i,j));
k2=h*f(t+h/2,wr(i,j)+k1/2);
k3=h*f(t+h/2,wr(i,j)+k2/2);
k4=h*f(t+h,wr(i,j)+k3);
wr(i+1,j)=wr(i,j)+(1/6)*(k1+2*k2+2*k3+k4);
end
error_we(j)=abs(we(n+1,j)-y(2));
error_wm(j)=abs(wm(n+1,j)-y(2));
error_wr(j)=abs(wr(n+1,j)-y(2));
end
% y=@(t)....
t=a:h(3):b;
plot(t,y(t),)

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