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(a) Apply the Euler method to find numerical solution for the first order ordinary differential equation given by dy := 5y+ey², y(0) = 2 , 0 <1<0.5 dt with the step size, h=0.1. (b) Calculate the true percentage error at every step size, when the exact solution is: 139e'5t _ 3e-21 )/3 y(t)=| 151 17

(a) Apply the Euler method to find numerical solution for the first order ordinary differential equation given by dy := 5y+ey², y(0) = 2 , 0 <1<0.5 dt with the step size, h=0.1. (b) Calculate the true percentage error at every step size, when the exact solution is: 139e'5t _ 3e-21 )/3 y(t)=| 151 17

Advanced Engineering Mathematics
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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(a) Apply the Euler method to find numerical solution for the first order ordinary differential equation given by dy := 5y+eªy², y(0)=2,0<1<0.5 dt with the step size, h=0.1. (b) Calculate the true percentage error at every step size, when the exact solution is: 139e'5t _ -21 )/3 151 - 3e y(t) = 17 (c) Apply the Fourth Order Runge-Kutta method to find x(t) at t = 0.2 of the second order initial value problem: d²x x ¸ dx di? dt -бх %3D0, х(0) %— 3, х'(0) %—D1, dx with step size At =h=0.2. Hint: Let y= dt
Transcribed Image Text:(a) Apply the Euler method to find numerical solution for the first order ordinary differential equation given by dy := 5y+eªy², y(0)=2,0<1<0.5 dt with the step size, h=0.1. (b) Calculate the true percentage error at every step size, when the exact solution is: 139e'5t _ -21 )/3 151 - 3e y(t) = 17 (c) Apply the Fourth Order Runge-Kutta method to find x(t) at t = 0.2 of the second order initial value problem: d²x x ¸ dx di? dt -бх %3D0, х(0) %— 3, х'(0) %—D1, dx with step size At =h=0.2. Hint: Let y= dt
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