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I Runge-Kutta method • Derive the third-order Runge-Kutta method (RK3). • Obtain the amplification factor of the RK3 method with the model equation y' = Ay. • Draw the stability regions of the second-, third- and fourth-order Runge-Kutta methods in the complex plane of Ah where h is the step size.

I Runge-Kutta method • Derive the third-order Runge-Kutta method (RK3). • Obtain the amplification factor of the RK3 method with the model equation y' = Ay. • Draw the stability regions of the second-, third- and fourth-order Runge-Kutta methods in the complex plane of Ah where h is the step size.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Please use python or matlab. Solution does not have to be perfect, just try your best. I Runge-Kutta method • Derive the third-order Runge-Kutta method (RK3). • Obtain the amplification factor of the RK3 method with the model equation y' = Ay. • Draw the stability regions of the second-, third- and fourth-order Runge-Kutta methods in the complex plane of Ah where h is the step size. • Consider the model problem, y' Xy where A = V-1. Identify the amplitude error and the phase error of the RK3 method. • Solve the following equation with RK2 and RK3 method and compare the numerical solution with the analytic solution. Use At = 0.2. y" + 4y = 0, t2 0 y(t = 0) = 1 y(t = 0) = 0
Transcribed Image Text:Please use python or matlab. Solution does not have to be perfect, just try your best. I Runge-Kutta method • Derive the third-order Runge-Kutta method (RK3). • Obtain the amplification factor of the RK3 method with the model equation y' = Ay. • Draw the stability regions of the second-, third- and fourth-order Runge-Kutta methods in the complex plane of Ah where h is the step size. • Consider the model problem, y' Xy where A = V-1. Identify the amplitude error and the phase error of the RK3 method. • Solve the following equation with RK2 and RK3 method and compare the numerical solution with the analytic solution. Use At = 0.2. y" + 4y = 0, t2 0 y(t = 0) = 1 y(t = 0) = 0
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