Explanation Given: d z d x + g ( x ) z 2 = f ( x ) where f ( x ) = 5 x + 2 and g ( x ) = x 2 which implies d z d x = 5 x − x 2 z 2 + 2 ∈ = 0.0001 . Approach: The recursive formulas for Runge-Kutta method are x n + 1 = x n + h , z n + 1 = z n + 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) , Where k 1 = h f ( x n + z n ) , k 2 = h f ( x n + h 2 , z n + k 1 2 ) , k 3 = h f ( x n + h 2 , z n + k 2 2 ) , k 4 = h f ( x n + h , z n + k 3 ) Calculation: Consider, k = z 0 = 1 The inputs are z 0 = 1 , x 0 = 0 , c = 1 f ( x , z ) = 5 x − x 2 z 2 + 2 The initial value for N in this algorithm is N = 1 , so h = ( c − x 0 N ) = ( 1 − 0 1 ) = 1 ∴ k 1 = h f ( x 0 , z 0 ) = 1 f ( 0 , 1 ) = 2 ,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 3.7, Problem 21E

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The solution of the given initial value problem at x=1.

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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 at x = 1 .

Solution Summary: The author approximates the solution of the given initial value problem at x=1 by using Runge-Kutta method.

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To approximate:

The solution of the given initial value problem at x=1.

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To approximate: The solution of the given initial value problem at x = 1 .

Solution Summary: The author approximates the solution of the given initial value problem at x=1 by using Runge-Kutta method.

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To approximate: The solution of the given initial value problem at x=1.

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Chapter 3 Solutions

To approximate:

The solution of the given initial value problem at x=1.