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Use the following methods with step size h= 1/5 to estimate y(1.6), where y(t) is the solution of the initial-value problem y=-y, 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= 1/5 to estimate y(1.6), where y(t) is the solution of the initial-value problem y=-y, 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 = 1/5 to estimate y(1.6), where y(t) is the solution of the initial-value problem y=-y, y(0) = 1. Find the absolute error in each case relative to the analytic solution y(t) = e-t. a) Euler method Result: Error: b) Implicit 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: Note: You can earn partial credit on this problem.
Transcribed Image Text:Use the following methods with step size h = 1/5 to estimate y(1.6), where y(t) is the solution of the initial-value problem y=-y, y(0) = 1. Find the absolute error in each case relative to the analytic solution y(t) = e-t. a) Euler method Result: Error: b) Implicit 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: Note: You can earn partial credit on this problem.
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