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Use the Runge-Kutta-Fehlberg method with tolerance TOL l()~6 , hmax 0.5, and hmin 0.05

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 3 Chapter 5.5

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 3

Use the Runge-Kutta-Fehlberg method with tolerance TOL l()~6 , hmax 0.5, and hmin 0.05 to approximate the solutionsto the following initial-value problems. Compare the results to the actual values. a. y' = y/r - (y/t)2 , 1 < r < 4, y(l) = 1; actual solution y(r) = r/(l + Inr). b. y' = 1 + y/r + (y/r)2 , I < r < 3, y(l) = 0; actual solution y(r) = rtan(lnr). c. y' = (y + l)(y-|-3), 0 < r < 3, y(0) =2; actual solution y(r) =-3-P2(1-t-e-2')-1 . d. y' = (r + 2r3 )y3 -ry, 0 < r < 2, y(0) = f; actual solution y(r) = (3 + 2r2 + 6e'2 ) _l/2 .

Step-by-Step Solution:
Step 1 of 3

L33 - 5 Fundamental Theorem of Calculus, Part II: If f is continuous on [a,b], then ▯ b f(x)dx = a ▯ where F is any antiderivative of f. (That is, F (x)= )

Step 2 of 3

Chapter 5.5, Problem 3 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Use the Runge-Kutta-Fehlberg method with tolerance TOL l()~6 , hmax 0.5, and hmin 0.05