A First Guide to Computational Modelling in Physics

The methods presented in this book primarily focus on differential
equations, both ordinary (ODE) and partial (PDE), while also covering
basic mathematical operations, derivatives, and quadrature, as intro­
duced in the second project (Diffraction on a Slit). The book addresses
typical problems such as initial value problems (IVP), boundary value
problems (BVP), and eigenvalue problems (EVP). Most of the methods
discussed are based on variable discretisation and recursive algorithms
for ODEs. For PDEs, the methods of finite difference (FD) and finite
elements (FE) are explained, along with selected matrix methods for
solving systems of equations (FD) and chosen iterative optimisation
methods (FE). In the case of PDEs, system symmetry is utilised to
reduce dimensionality from 3D to 1D, simplifying implementation and
allowing projects to be completed within reasonable time constraints.