3 papers
math.NA2026
DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains
Anshima Singh, David J. Silvester
Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed…
math.NA2023
Error analysis of a high-order fully discrete method for two-dimensional time-fractional convection-diffusion equations exhibiting weak initial singularity
Anshima Singh, Sunil Kumar
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is empl…
math.NA2022
An efficient numerical method based on exponential B-splines for time-fractional Black-Scholes equation governing European options
Anshima Singh, Sunil Kumar
In this paper a time-fractional Black-Scholes model (TFBSM) is considered to study the price change of the underlying fractal transmission system. We develop and analyze a numerica…