This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical ...

In this study, an accurate analytical solution is presented for fuzzy FPDEs. It is done by using a novel method called the Laplace-residual power series (LRPSM) to build a series solution to the given ...

Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, ...

Partial Differential Equations Preliminary Exam Syllabus Formula-sheet (PDF) for the exam. Texts M Shearer and R Levy (2015) Partial Differential Equations (Chapters 1-9) LC Evans (1997) Partial ...

My research interests are in applied and computational mathematics. I am interested in developing and analyzing high-order numerical methods for solving partial differential equations and fractional ...