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
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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.

dy
dx
=
4x3 + 6x2 – 5x + 3
Transcribed Image Text:dy dx = 4x3 + 6x2 – 5x + 3
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