Abstract: In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one ...

THE teaching of differential equations in English universities usually follows an unsatisfactory middle path. General theory is omitted as too difficult, while numerical methods are considered ...

Abstract: In this paper, we present a robust and accurate numerical method for solving the generalized Black–Scholes equation governing option pricing. We use a horizontal method of lines to ...

Great for teaching/learning numerical methods step by step. Good reference for people writing their own solvers in C/Fortran/Julia. Lightweight, no dependencies. Consistent object-oriented API (.solve ...

Python project that implements a mean‑field approach to derive differential equations that simulate extended Schelling models and generate iterative time‑series data for the most important parameters.