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Consider the following first order ordinary differential equation (ODE): dy = X dx ху 2 from x=1 to x=3.4 with y(1)=1 a. Solve with Euler's method using h=0.8 b. Solve with fourth-order Runge-Kuta method using h=0.8 1-x2 The analytical solution of the ODE is y = 2 – e In each part, calculate the error between the analytical and the numerical solution at the points where the numerical solution is determined.

Consider the following first order ordinary differential equation (ODE): dy = X dx ху 2 from x=1 to x=3.4 with y(1)=1 a. Solve with Euler's method using h=0.8 b. Solve with fourth-order Runge-Kuta method using h=0.8 1-x2 The analytical solution of the ODE is y = 2 – e In each part, calculate the error between the analytical and the numerical solution at the points where the numerical solution is determined.

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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Consider the following first order ordinary differential equation (ODE): dy xy = x - dx 2 from x=1 to x=3.4 with y(1)=1 a. Solve with Euler's method using h=0.8 b. Solve with fourth-order Runge-Kuta method using h=0.8 1-x2 The analytical solution of the ODE is y = 2 – e 4 In each part, calculate the error between the analytical and the numerical solution at the points where the numerical solution is determined.
Transcribed Image Text:Consider the following first order ordinary differential equation (ODE): dy xy = x - dx 2 from x=1 to x=3.4 with y(1)=1 a. Solve with Euler's method using h=0.8 b. Solve with fourth-order Runge-Kuta method using h=0.8 1-x2 The analytical solution of the ODE is y = 2 – e 4 In each part, calculate the error between the analytical and the numerical solution at the points where the numerical solution is determined.
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