Python or MATLAB

Question is as follows:

NOTE:

Python is not required, MATLAB may be used.

Subject: Numerical Methods for Ordinary Differential Equations: Initial Value Problems.

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Useful Information

= the time-step size.

= The solution, where the superscript refers to the time step. It is assumed that the time step is known and is the next unknown time step.

= the absolute error .

= the error ratio.

Taylor Series Method of Order 2:

Note: This is the not the "Taylor series method of order 4" required in the question, but this helps with understanding the general order P method (also posted down below).

Taylor Series Method of Order P:

2. Consider the following initial value problem (IVP): 0