Question

1. Apply Euler's Method with step size h=0.1 on [0, 1] to the initial value problems in Exercise 3. Print a table of the t values, Euler approximations, and error (difference from exact solution) at each step.

Exercise 3 is used towards the question. Please in MATLAB coding.

Answer 1

a)

clc

clear all

close all

format short

f=@(t,y) t;

[T,Y]=eulerSystem(f,[0,1],1,0.1);

T=T(:);

Y=Y(:);

table(T,Y)

function [t,y]=eulerSystem(Func,Tspan,Y0,h)

t0=Tspan(1);

tf=Tspan(2);

N=(tf-t0)/h;

y=zeros(length(Y0),N+1);

y(:,1)=Y0;

t=t0:h:tf;

for i=1:N

y(:,i+1)=y(:,i)+h*Func(t(i),y(:,i));

end

end

b)

clc

clear all

close all

format short

f=@(t,y) t^2*y;

[T,Y]=eulerSystem(f,[0,1],1,0.1);

T=T(:);

Y=Y(:);

table(T,Y)

function [t,y]=eulerSystem(Func,Tspan,Y0,h)

t0=Tspan(1);

tf=Tspan(2);

N=(tf-t0)/h;

y=zeros(length(Y0),N+1);

y(:,1)=Y0;

t=t0:h:tf;

for i=1:N

y(:,i+1)=y(:,i)+h*Func(t(i),y(:,i));

end

end