3 papers
math.NA2026
Characteristic Based Physics Informed Neural Networks for Advection Equations with a Focus on Discontinuous Solutions
Omid Khosravi, Mehdi Tatari
This paper presents a characteristic-based loss function for physics-informed neural networks (PINNs) that circumvents automatic differentiation and significantly reduces training…
math.NA2020
Computing exponential of tridiagonal Toeplitz matrices with applications to numerical solution of the heat equation
Mehdi Tatari, Majed Hamadi
The computation of the exponential of a tridiagonal matrix and its applications have always been of interest. One application considered here is when the method of lines is used to…
math.NA2018
Error and Stability Estimates of a Least-Squares Variational Kernel-Based Method for Second Order Elliptic PDEs
Salar Seyednazari, Mehdi Tatari, Davoud Mirzaei
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this se…