This document contains the solutions to a numerical methods assignment. The solutions include Python code implementations for Euler's method, the Runge-Kutta 4th order method, and a finite difference method for solving the diffusion equation. The assignment covers topics such as solving ordinary differential equations (ODEs) and partial differential equations (PDEs) numerically. The solutions provide estimated values, Python code, and plots illustrating the results of each method. Specifically, the document includes solutions for Assignment 4, which explores Euler's method; Assignment 5, which involves solving a diffusion equation; and a quiz question demonstrating the effect of step size on approximation accuracy using Euler's method. The Python code allows for the visualization of the results and comparison of the numerical solutions with the exact solutions where available.
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