Extend scipy.integrate with various methods for solve_ivp

Implementations of various Algorithms used in Numerical Analysis, from root-finding up to gradient descent and numerically solving PDEs.

The aim of this research is to develop an effective numerical method that can be used to efficiently compute surges in pipes due to valve connecting two reservoirs being rapidly opened, using a computer program developed in the Python environment.

Collection of fixed-step IVP solvers. Includes support for matrix-valued IVPs, and provides functions for generating IVP solver equations.

Using the Adams-Bashforth-Moulton method (with Runge-Kutta 4th order) to approximate the Lorenz problem. 3D result plotting using matplotlib.

I have tried to explain the multi-step-methods of solving ODEs via Adams-Bashforth and Adams-Moulton methods which are explicit and implicit methods respectively. I also have implemented them explicitly to solve for a system of ODEs, I have also done an explicit implementation of fourth order Runge-Kutta method in the process as it is needed.