Develop the following differential equation analytically and numerically, using Euler's method, modified Euler and Runge Kutta fourth order: From x=0 to x=4, with a step size of 0.25. the initial condition indicates that for x=0, y=1. Show the results using a table where all the results are compiled. Generate, in the same way, the percentage errors that accumulate in each of the methods. Note: Remember to evaluate the true "y" to be able to compare the mathematical models used.
Develop the following differential equation analytically and numerically, using Euler's method, modified Euler and Runge Kutta fourth order: From x=0 to x=4, with a step size of 0.25. the initial condition indicates that for x=0, y=1. Show the results using a table where all the results are compiled. Generate, in the same way, the percentage errors that accumulate in each of the methods. Note: Remember to evaluate the true "y" to be able to compare the mathematical models used.
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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Develop the following differential equation analytically and numerically, using Euler's method, modified Euler and Runge Kutta fourth order:
From x=0 to x=4, with a step size of 0.25. the initial condition indicates that for x=0, y=1.
Show the results using a table where all the results are compiled. Generate, in the same way, the percentage errors that accumulate in each of the methods.
Note: Remember to evaluate the true "y" to be able to compare the mathematical models used.
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