a) Consider the initial value problem(IVP); dy + y cos x = dx 1 sin 2x, y(0) = 1 %3D Approximate y(0.5) by using; i. Taylor series method of order 2 with h = 0.25. ii. fourth order Runge-Kutta method with step size h = 0.5. Given the exact solution for the IVP is y = sinx-1+2e-sinx, Compute the absolute error for both calculation in (i) and (ii), then state one suggestion to reduce the error for calculation in (i).
a) Consider the initial value problem(IVP); dy + y cos x = dx 1 sin 2x, y(0) = 1 %3D Approximate y(0.5) by using; i. Taylor series method of order 2 with h = 0.25. ii. fourth order Runge-Kutta method with step size h = 0.5. Given the exact solution for the IVP is y = sinx-1+2e-sinx, Compute the absolute error for both calculation in (i) and (ii), then state one suggestion to reduce the error for calculation in (i).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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