Runge-Kutta method (Order 4) for solving ODE using MATLAB

In each of the following exercises, use the Runge-Kutta method to approximate the solution of the initial value problem in the given interval. In Exercises 2 through 6 compare the approximate values with the correct values obtained by elementary methods. Continue the computation of Example 3.1 to obtain approximate values of y for x=0.3,0.4, and 0.5 . | Numerade

1.15 points Consider the 3rd-order Runge-Kutta algorithm below:... | Filo

SOLVED:Using the vectorized Runge-Kutta algorithm, approximate the solution to the initial value problem y^n=t^2 y^2 ; y(0)=1, y^'(0)=0 at t=1 1. Starting with h=1, continue halving the step size until two successive approximations [of both y(1) and y^'(1)] differ by at most 0.01.

SOLVED:(a) Use a numerical integration algorithm such as a Runge-Kutta method to compute the density profile for the n=1.5 and n=3 polytropes. Be sure to correctly incorporate the boundary conditions in your integrations. (b) Plot your results and compare them with the n=0, n=1, and n=5 analytic models determined in Problem 20.