Numerical Analysis Assignment with Source Code: ODE Experiments and Extensions

This numerical analysis assignment with source code comprises two main sections: three experimental problems on ordinary differential equations (ODEs) and extended discussions covering higher-order ODE solutions and boundary value problems (BVP). All algorithms and computational examples are implemented using MATLAB. The assignment classifies ODE problems based on stiffness - non-stiff problems yield excellent results with ODE45, while stiff problems (like large-coefficient VDP equations) require specialized solvers like ODE15S for efficient computation. The document explores various numerical methods including state-space transformations for higher-order equations, step-size selection strategies, and compares Adams multistep methods with Runge-Kutta approaches.