Linear Multistep solver for differential equations

Linear Multistep solver for differential equations + Newton's method & order of convergence analysis

Numerical Methods for solving differential equations

The coefficients a_j and b_j are real and fully identify the method, as explained in the file.

At the end of the code you can check the parameter values for the following methods:

1. Adam-Bashforth (AB, Explicit Adam)
2. Adam-Moulton (AM, Implicit Adam)
3. Backward Differentiation Methods (BDF, Implicit)

If you want to check solutions I recommend using ODE45 (which approximates through Runge-Kutta4) and plotting the error by subtraction.

Reference:

Quarteroni, A., Sacco, R., & Saleri, F. (2010). Numerical mathematics (Vol. 37). Springer Science & Business Media.

11.5 - Multistep Methods: (11.45)