Q4 (a) (b) Consider the first order initial value problem dy dx (i) Approximate the solution of the problem at x = 0.05,

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Q4 A B Consider The First Order Initial Value Problem Dy Dx I Approximate The Solution Of The Problem At X 0 05 1 (36.04 KiB) Viewed 24 times

Q4 (a) (b) Consider the first order initial value problem dy dx (i) Approximate the solution of the problem at x = 0.05, 0.1 and 0.15 using Euler's method. = 2x+e", (ii) Fourth order Runge-Kutta method. y (0)=1. (i) (7 marks) Please use a suitable value of stepsize, h and give your answer in three decimal places. (ii) Given the second order boundary value problem y" + 4y = sinx, y(0) = 0, y(1)=0. By taking h=0.25, approximate y(0.25), y(0.5) and y(0.75) by finite difference method. Please give your answer in three decimal places. (10 marks) (6 marks) If the exact solution of the problem is y(x) = - the absolute errors of your calculations. sin (1) 3sin (2) -sin 2x+-sinx, find 3 (2 marks)