Using Runge-Kutta method of order 4, find y for x=0.1,0.2,0.3 given that , )0( ;.1 2 = y + xy y
Using Runge-Kutta method of order 4, find y for x=0.1,0.2,0.3 given that , )0( ;.1 2 = y + xy y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12. Using Runge-Kutta method of order 4, find y for x=0.1,0.2,0.3 given that , )0( ;.1 2 = y + xy y.
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12. Using Runge-Kutta method of order 4, find y for x=0.1,0.2,0.3 given that , )0( ;.1 2 = y + xy y = dx dy and also find the solution at x=0.4 using Milne’s method. (16) 13.a. Given 1( ), )1( ,1 )1.1( .1 233, )2.1( .1 548, )3.1( .1 979, 2 = x + y y = y = y = y = dx dy evaluate y(1.4) by Adams – Bashforth method. (8) b. Given , )0( ;.1 2 = y - x y = dx dy y(0.2) = 1.1218 y(0.4) = 1.4682 y(0.6) = 1.7379 estimate y(0.8) by Adam’s method (8) 14. Consider the initial value problem ,1 )0( .5.0 2 = y - x + y = dx dy (16) a. Using the modified Euler method, find y(0.2) b. Using 4th order Runge-Kutta method, find y(0.4) and y(0.6) c. Using Adam-Bashforth Predictor- Corrector method. Find y(0.8).
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