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Part I (50%) Show that the Modi ed Euler method is of order two. Use Theorem 5.20 to show that the Runge-Kutta method of order four is consistent. Exercise 5.10.4 a,b,c,d Exercise 5.4.30. Exercise 5.4.32. Part II (50%) Consider the following well-posed IVP: 8 y0(t) =…
Consider the following well-posed IVP:
8 | y0(t) = 1 + | y | ; 1 | t 2; | (1) |
t | |||||
< |
with the exact solution y(t) = t ln t + 2t. Choose the step sizes h = 0:2; 0:1; 0:05, respectively.
order of the method from the error. Which value of h do you need to choose (approximately) to achieve an accuracy of 10 4 for y(2)?
Requirements
Submit the code le to CCLE : A MATLAB (or other software) function taylor2.m that implements Taylor’s method of order two, a MATLAB function (or other software) midpt.m that implements Mid-point method, and a MATLAB (or other software) script main.m that solves the IVP (1) and plots the approximated solutions versus the exact one.
Print a PDF report to your TA.
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