Explanation Given: y ' = 3 Cos ( y − 5 x ) , y ( 0 ) = 0 , h = 0.1 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 = 0 , c = 0 f ( x , y ) = 3 Cos ( y − 5 x ) At x = 0 The initial value for N in this algorithm is N = 1 , so h = ( c − x 0 N ) = ( 0 − 0 1 ) = 0 ∴ k 1 = h f ( x 0 , y 0 ) = 0.1 f ( 0 , 0 ) = 0.3 , k 2 = h f ( x 0 + h 2 , y 0 + k 1 2 ) = 0.1 f ( 0.05 , 0.5 ) = 0.299997 k 3 = h f ( x 0 + h 2 , y 0 + k 2 2 ) = 0.1 f ( 0.05 , 0.149998 ) = 0.299999 k 4 = h f ( x 0 + h , y 0 + k 3 ) = 0

7th Edition

ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

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Differential Equations

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Chapter 3.7, Problem 16E

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The solution of the given initial value problem at x=0, 0.1, 0.2, ..., 4.

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Chapter 3.7, Problem 15E

Chapter 3.7, Problem 17E

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To approximate: The solution of the given initial value problem at x = 0 , 0.1 , 0.2 , ... , 4 .

Solution Summary: The author explains how Runge-Kutta method approximates the solution of the given initial value problem.

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To approximate:

The solution of the given initial value problem at x=0, 0.1, 0.2, ..., 4.

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Chapter 3 Solutions

To approximate: The solution of the given initial value problem at x = 0 , 0.1 , 0.2 , ... , 4 .

Solution Summary: The author explains how Runge-Kutta method approximates the solution of the given initial value problem.

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To approximate: The solution of the given initial value problem at x=0, 0.1, 0.2, ..., 4.

Want to see the full answer?

Chapter 3 Solutions

To approximate:

The solution of the given initial value problem at x=0, 0.1, 0.2, ..., 4.