Matlab code for ODE problems

I have the function (dy/dt)=-t*e^y, y(0)=0 and have to create a code using four seperate methods (Euler, Huen, Modified Euler, and RK4) in order to graph the four different method's y values from time t (-5,5) and 1 second intervals.

I created a code with each method however I cannot get them to work even individually let alone all together.

Any help would be appreciated.

clear all
close all
clc
k=1;
t=-5:k:5
y=zeros([11 1])
y(1)=1
n=numel(y)
% Euler Method
    for i=1:n-1
        y(i+1)=y(i)-t*exp(y(i))*k  
    end
% Huen Method
for i=1:n-1
    fs=-t*exp(y(i))
    yp(i+1)=y(i)-fs*k
    fe=-t*exp(yp(i+1))
    y(i+1)=y(i)+(1/2)*(fs+fe)*k
end
% Modifier Euler Method
for i=1:n-1
    y(i+1/2)=y(i)-t*exp(y(i))*(k/2)
    y(i+1)=y(i)-t*exp(y(i))*k
end
% RK4
for i=1:n-1
    f1=-t*exp(y(i))
    f2=-(t+k/2)*exp(y(i)+.5*f1*k)
    f3=-(t+k/2)*exp(y(i)+.5*f2*k)
    f4=-(t+k)*exp(y(i)+f3*k)
    Qk=(1/6)*(f1+2*f2+2*f3+f4)
    y(i+1)=y(i)+Qk*k
end
plot(t,y);
grid on

Answer 1

[Pratyush Roy]

Hi Garrett,

For all the methods for solving ODEs, the time as well as variable should change in steps. Considering the code snippet for the Euler method:

y(i+1)=y(i)-t*exp(y(i))*k 

The right hand side of the equation contains multiplication of y(i) with vector t which gives us a vector but that is assigned to a scalar value y(i+1).The time values should also vary in steps with the functional value y(i). The following code snippet demonstrates the case where both time and functional value is varying:

y(i+1)=y(i)-t(i)*exp(y(i))*k

The same changes are applicable for the other techniques as well.

Hope this helps!

Regards,

Pratyush.