a) Consider the initial value problemdydx√y(4x + 2) = 0, y(0) = 1.i. Approximate y(0.5) by using Taylor's method order 2 with step size h = 0.5.ii. Evaluate y(1.0) by using fourth-order Runge-Kutta method with step size h = 1.

Given:i. Find approximate value by using Tylor's method order 2 with .ii. We have to find by using…

Answered: a) Consider the initial value problem…

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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A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar’s initial temperature is given by the function f(x) = 200 - 30x degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x,t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x,t) and then u5(2, 0.1).

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a) Consider the initial value problem dy √y(4x +2)= 0, y(0) = 1. dx i. Approximate y(0.5) by using Taylor's method order 2 with step size h = 0.5. - ii. Evaluate y(1.0) by using fourth-order Runge-Kutta method with step size h = 1.