Hey everyone I need to construct a matlab program that implements the fourth ord

ID: 2971014 • Letter: H

Question

Hey everyone I need to construct a matlab program that implements the fourth order Runge-kutta

it should be able to implement the fourth order runge-kutta for ivps of the form

y^1=f(y,t)

y(t0)=y0

It should have a data function at the end of the .m file that allows users to input values for

f(y,t),t0,y0,N and h, h being step size and N the number of steps to reach endpoint

the program should output the approximations of y(ti)(i.e.{w0,w1...wn})

should also include a graphical approximation to the solution.

the program should be coded with

y^1=2/t*y+t^2e^t

y(1)=0

h=.1

N=10

*dont think its a long code, but Im matlab challenged

clc; % Clears the screen

clear all;

h=0.1; %step size

N=10; %no of points

l=N*h;

t(1)=0.1;

for i=1:1:N-1 %calculating t-axis

t(i+1)=(i+1)*h;

end;

y = zeros(1,length(t));

y(1) = 0; % initial condition

F_ty = @(t,y) (((2/t)*y)+(t^2)*(exp(t))); % change the function as you desire

for i=1:(length(t)) % calculation loop

k_1 = F_ty(t(i),y(i));

k_2 = F_ty(t(i)+0.5*h,y(i)+0.5*h*k_1);

k_3 = F_ty((t(i)+0.5*h),(y(i)+0.5*h*k_2));

k_4 = F_ty((t(i)+h),(y(i)+k_3*h));

y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; % main equation

fprintf('t(%d) = %f -> y(%d) = %f ',i,t(i),i,y(i));%displaying the values

end