In python code please, do not test on example on page 315. Use code from number

Question

In python code please, do not test on example on page 315. Use code from number 1 to implement number 2.

Write a Python program to implement the Runge-Kutta Method of order 4 to approximate the value of the solution of the differential equation x'(t) = f(t, x) x(a) = xa at t = b using n steps. The definition statement of your program should be def RK4 (f a, b, xa, n) Your output statement should be of the form: The approximate value of the solution at x = bbb is SSSS. where bbb is the value b and SSSS is the solution value. Test your program on the example at the bottom of page 315. Consider the differential equation x' = (2 - t)x with x (2) = 1. Use your Runge-Kutta code to approximate the solution at t 3 with the following step sizes: t = 2^-k for k = 0, 1,, 6. The exact solution is x(t) = e^-(1/2)(t - 2)^2 Compute the error in each approximation and the ratio of the errors with the previous value of t (for example error(t = 2^-1)/ error (t = 2^-0) error (t = 2^-2)/error (t = 2^-1)). Explain what the ratios tell you about the order of the method.

Explanation / Answer

:param xvinit: A list of starting values.
:param Tmax: Step size.
:param N: Endpoint.
:param f : Functions

=======================================================

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.