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Q 3.7-9E

Fundamentals Of Differential Equations And Boundary Value Problems
Found in: Page 139
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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Short Answer

Use the fourth-order Runge–Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem y'=x+1-y,y(0)=1, at x = 1. Compare this approximation with the one obtained in Problem 5 using the Taylor method of order 4.


See the step by step solution

Step by Step Solution

Step 1: Find the values of ki, i = 1, 2, 3, 4

Since f(x,y)=x+1-y and x = 0, y = 1, and h = 0.25

role="math" localid="1664324055813" k1=hf(x,y)=0.25(0+1-1)=0k2=hfx+h2,y+k12=0.03125k3=hfx+h2,y+k22=0.0273438k4=hfx+h,y+k3=0.0556641

Step 2: Find the values of x and y


Step 3: Use values of x and y for finding values of ki, i = 1, 2, 3, 4




Step 4: Repeat the procedure for two times




Therefore ϕ(1)=1.3679

Hence the solution is ϕ(1)=1.3679

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