Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can ...

The PIML4PDE framework is designed to solve Partial Differential Equations (PDEs) using Physics-Informed Machine Learning (PIML). This framework is intended for educational purposes, demonstrating ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Abstract: The numerical solution of coupled partial differential equations (PDEs) represents a significant challenge for traditional methods such as the finite element method (FEM), particularly in ...