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

Fundamentals of Differential Equations [With CDROM] - 7th Edition

7th Edition

ISBN: 9780321410481

Author: Saff, Edward B., Snider, Arthur David, Nagle, R. Kent

Publisher: Addison Wesley

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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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Fundamentals of Differential Equations [With CDROM] - 7th Edition

Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A swimming pool whose volume is 10,000gal contains...Ch. 3.2 - The air in a small room 12ft by 8ft by 8ft is 3...Ch. 3.2 - Beginning at time t=0, fresh water is pumped at...Ch. 3.2 - A tank initially contains S0lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Prob. 10E

Ch. 3.2 - Prob. 11E Ch. 3.2 - For the logistic curve15, assume pa:=p(ta) and...Ch. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - 16 Show that for a differentiable function p(t),...Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - A snowball melts in such a way that the rate of...Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - During the summer the temperature inside a van...Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.4 - Prob. 1E Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 7E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 9E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - In Problem 16, let I=50 kg-m2 and the retarding...Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Rocket Flight. A model rocket having initial mass...Ch. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - An RL circuit with a 5- resistor and a 0.05-H...Ch. 3.5 - Prob. 2E Ch. 3.5 - The pathway for a binary electrical signal between...Ch. 3.5 - If the resistance in the RL circuit of Figure...Ch. 3.5 - Prob. 5E Ch. 3.5 - 6. Derive a power balance equation for the RL and...Ch. 3.5 - 7. An industrial electromagnet can be modeled as...Ch. 3.5 - 8. A 108F capacitor 10 nanofarads is charged to 50...Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - In Example 1, page 126, the improved Eulers method...Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Use the improved Eulers method subroutine with...Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Use the improved Eulers method with tolerance to...Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - The solution to the initial value problem...Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 20E Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Prob. 3E Ch. 3.7 - Prob. 4E Ch. 3.7 - Prob. 5E Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Prob. 9E Ch. 3.7 - Prob. 10E Ch. 3.7 - Prob. 11E Ch. 3.7 - Prob. 12E Ch. 3.7 - Prob. 13E Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - The Taylor method of order 2 can be used to...Ch. 3.7 - Prob. 18E Ch. 3.7 - Prob. 19E Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E

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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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Videos

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.