Monge–Ampère equation: A fully nonlinear partial differential equation characterised by the determinant of the Hessian matrix of a function, playing a fundamental role in complex differential ...

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, 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 ...

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

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 ...

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

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 ...

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

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 ...

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