An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and ...

1 Institute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou, China 2 School of Mathematics and Statistics, Huaibei Normal University, Huaibei, China This study introduces a ...

A method for the numerical solution of the n-point boundary value problem for homogeneous linear ordinary differential equations is developed. The method requires two Runge-Kutta integrations over the ...

Abstract: This paper investigates a distinct numerical algorithm for the solution of first and second orders initial value problems. The new method was developed using interpolation and collocation ...

\texttt{DiscoTEX} is a highly accurate numerical algorithm for computing numerical weak-form solutions to distributionally sourced partial differential equations (PDE)s. The aim of this second paper, ...

A formula for numerical integration is prepared, which involves an exponential term. This formula is compared to two standard integration methods, and it is shown that for a large class of ...

Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential ...

1 Department of Mathematics, National Institute of Technology, Kurukshetra, India 2 Department of Mathematics, Pt. CLS. Govt. PG College, Karnal, India The aim of the present work is to devote a ...