Consider the initial-value problem y = 6x + y, y(0) = 7. Calculate the first step only (i.e., y₁) of the numerical solution using (i) the forward Euler method, (ii), the Improved Euler Method and (iii) the Runge-Kutta method of order 4, all with h = 0. 1. Compare the approximations with the true values by calculating the simple errors |true - approx.
Consider the initial-value problem y = 6x + y, y(0) = 7. Calculate the first step only (i.e., y₁) of the numerical solution using (i) the forward Euler method, (ii), the Improved Euler Method and (iii) the Runge-Kutta method of order 4, all with h = 0. 1. Compare the approximations with the true values by calculating the simple errors |true - approx.
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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Transcribed Image Text:Question 11
Consider the initial-value problem
y = 6x + y,
y(0) = 7.
Calculate the first step only (i.e., y₁) of the numerical solution using (i) the forward
Euler method, (ii), the Improved Euler Method and (iii) the Runge-Kutta method of
order 4, all with h : 0. 1. Compare the approximations with the true values by
calculating the simple errors true - approx.
-
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