Explanation Given: The given initial value problem is, y ' = 1 − x y , y ( 1 ) = 1 . Formula used: The classical fourth-order Runge-kutta method is defined as, k 1 = h f ( x , y ) k 2 = h f ( x + h 2 , y + k 1 2 ) k 3 = h f ( x + h 2 , y + k 2 2 ) k 4 = h f ( x + h , y + k 3 ) Calculation: From the given initial value problem, x 0 = 0 , y 0 = 1 , c = 2 , ∈ = 0.001 . f ( x , y ) = 1 − x y For N = 1 h = 1 − 0 1 = 1 By Runge-Kutta method, k 1 = h f ( x , y ) = h ( 1 − x y ) = 1 ( 1 − ( 1 ) ( 1 ) ) = 0 k 2 = h f ( x + h 2 , y + k 1 2 ) = 1 ( 1 − ( 1 + 1 2 ) ( 1 + 0 ) ) = − 1 2 k 3 = h f ( x + h 2 , y + k 2 2 ) = 1 ( 1 − ( 1 + 1 2 ) ( 1 − 5 8 ) ) = − 1 8

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 10E

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The approximate solution to the initial values problem y'=1−xy,y(1)=1 using Runge-Kutta subroutine.

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Chapter 3.7, Problem 9E

Chapter 3.7, Problem 11E

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Fundamentals of Differential Equations and Boundary Value Problems

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To state: The approximate solution to the initial values problem y ' = 1 − x y , y ( 1 ) = 1 using Runge-Kutta subroutine.

Solution Summary: The author states the approximate solution to the initial values problem y(2)=0.70139 using Runge-Kutta subroutine.

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To state:

The approximate solution to the initial values problem y'=1−xy,y(1)=1 using Runge-Kutta subroutine.

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Chapter 3 Solutions

To state: The approximate solution to the initial values problem y ' = 1 − x y , y ( 1 ) = 1 using Runge-Kutta subroutine.

Solution Summary: The author states the approximate solution to the initial values problem y(2)=0.70139 using Runge-Kutta subroutine.

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To state: The approximate solution to the initial values problem y'=1−xy,y(1)=1 using Runge-Kutta subroutine.

Want to see the full answer?

Chapter 3 Solutions

To state:

The approximate solution to the initial values problem y'=1−xy,y(1)=1 using Runge-Kutta subroutine.