Runge Kutta Method With Matlab

PLEASE HELP ME :)

Consider the initial value problem

y’ = t^2 + y^2, y(0) = 1.

Use the Runge-Kutta method or another method to find approximate values of the solution at t = 0.8,0.9,and 0.95. Choose a small enough step size so that you believe your results are accurate to at least four digits.

Use MatLab

Thankyou:)

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

[Rifan Sinaga]

I got this answer, when I compared it manually, the results didn't same

f = @(t, y) t^2 + y^2;
yn= 0; tn = 0;
h = input('for h = ');
tf= 1;
n = tf/ h;
fprintf('  t         y\n');
fprintf('%.3f    %.7f\n', tn, yn);
for k = 1:n
    k1 = f(tn, yn);
    k2 = f(tn + h/2, yn + h * (k1/2));
    k3 = f(tn + h/2, yn + h * (k2/2));
    k4 = f(tn + h, yn + h * k3);
    yn = yn + h * (k1 + 2 * k2 + 2 * k3 + k4)/6;
    tn = tn + h;
    fprintf('%.2f    %.5f\n', tn, yn);
    plot(tn,yn,'r+');
    grid on; hold on;
end

[Rifan Sinaga]

Finally, i can solbe this problem

[darova]

Your solution is correct. YOu can check it using ode45 built-in solver

[t,y] = ode45(f,[0 1],0);
plot(t,y)

Answer 1

[Rifan Sinaga]

Help please