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Use the following methods with step size h=1/4 to estimate y(2), where y(t) is the solution of the initial-value problem =-y, (0)= 1. Find the absolute error in each case relative to the analytic solution y(t) e a) Euler method Result: Error:

Use the following methods with step size h=1/4 to estimate y(2), where y(t) is the solution of the initial-value problem =-y, (0)= 1. Find the absolute error in each case relative to the analytic solution y(t) e a) Euler method Result: Error:

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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Use the following methods with step size h= 1/4 to estirmate y(2), where y(t) is the solution of the initial-value problem =, (0) 1. Find the absolute error in each case relative to the analytic solution y(t) e a) Euler method Result: Error: b) Implick Euler method Result: Error: c) Crank-Nicolson method Result: Error: d) RK2 (Heun's method) Result: Error: e) RK4 (Classical 4th-Order Runge-Kutta method) Result: Error:
Transcribed Image Text:Use the following methods with step size h= 1/4 to estirmate y(2), where y(t) is the solution of the initial-value problem =, (0) 1. Find the absolute error in each case relative to the analytic solution y(t) e a) Euler method Result: Error: b) Implick Euler method Result: Error: c) Crank-Nicolson method Result: Error: d) RK2 (Heun's method) Result: Error: e) RK4 (Classical 4th-Order Runge-Kutta method) Result: Error:
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