We then obtain the exact solutions of nonhomogeneous Riemann-Liouville fractional differential equations with pure delay. In addition, this paper explores the Hyers-Ulam stability of nonhomogeneous ...

The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...

The course provides a thorough introduction to design, analysis (both theoretical and empirical), and programming of difference and elemental methods to solve differential equations. In addition, the ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Firstly, the coupled Gross-Pitaevskii equations are changed into a nonlinear coupled ordinary differential system by a coupled traveling wave solution transformation. Secondly, by using the modified ...

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 ...