Explanation Given: y ' = y Cos x, y ( 0 ) = 1 , absolute tolerance, ∈ = 0.01 Approach: The recursive formulas for Runge-Kutta method are x n + 1 = x n + h , y n + 1 = y n + 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) , Where k 1 = h f ( x n + y n ) , k 2 = h f ( x n + h 2 , y n + k 1 2 ) , k 3 = h f ( x n + h 2 , y n + k 2 2 ) , k 4 = h f ( x n + h , y n + k 3 ) The inputs are x 0 = 0 , y 0 = 1 , c = π , ∈ = 0.01 f ( x , y ) = y Cos x Consider, z = y 0 = 1 The initial value for N in this algorithm is N = 1 , so h = ( c − x 0 N ) = ( π − 0 1 ) = π ∴ k 1 = h f ( x 0 , y 0 ) = π f ( 0 , 1 ) = π ,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Differential Equations

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Chapter 3.7, Problem 14E

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The solution of the given initial value problem x=π.

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Fundamentals of Differential Equations and Boundary Value Problems

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To approximate: The solution of the given initial value problem x = π .

Solution Summary: The author approximates the solution of the given initial value problem x=pi by using Runge-Kutta method.

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To approximate:

The solution of the given initial value problem x=π.

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Chapter 3 Solutions

To approximate: The solution of the given initial value problem x = π .

Solution Summary: The author approximates the solution of the given initial value problem x=pi by using Runge-Kutta method.

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To approximate: The solution of the given initial value problem x=π.

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Chapter 3 Solutions

To approximate:

The solution of the given initial value problem x=π.