Nonlinear partial differential equations (PDEs) characterise a wide range of complex phenomena in science and engineering, from fluid dynamics to signal processing in biomedical systems. In recent ...

In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one-dimensi ...

In this paper, the concept of multirate partial differential equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The ...

5 + Years Experience IT - Software Development Reservoir Engineering Software Specialist Posted: July 04, 2025 ...

In this paper, lump solutions of nonlinear partial differential equations, the generalized (2 + 1)-dimensional KP equation and the Jimbo–Miwa equation, are studied by using the Hirota bilinear method ...

Learning data-driven discretizations for partial differential equations Code associated with the paper: Learning data-driven discretizations for partial differential equations. Yohai Bar-Sinai, ...

3 Hermite spectral scheme for the logistic model This section is for application of the Hermite spectral approximation to the Logistic equation in two-dimensions. We construct a Hermite spectral ...

Course content The course provides an introduction to the theoretical basis for linear partial differential equations, focusing on elliptic equations and eigenvalue problems. The techniques and ...

Course content 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 ...

This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of ...

A collection of resources about partial differential equations, deep learning, graph neural networks, dynamic system simulation. We also roughly categorize the resources into the following categories ...

University of Utah engineers encode partial differential equations in light and feed them into newly designed optical neural engine, or ONE, to accelerate machine learning.