This analog computer on a chip is useful for certain kinds of operations that CPUs are historically not efficient at, including solving differential equations. Other applications include matrix ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial value problems - ...

This is the 2nd part of a two course graduate sequence in analytical methods to solve partial differential equations of mathematical physics. Review of Separation of variables. Laplace Equation: ...

Discontinuous Galerkin (DG) methods are a class of numerical techniques used to solve partial differential equations (PDEs). These methods are particularly useful for problems where traditional ...

More information: Leticia Mattos Da Silva et al, A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains, ACM Transactions on Graphics (2024). DOI: 10.1145/3666087 ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

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, ...

The study of wave phenomena by means of mathematical models often leads to a certain class of nonlinear partial differential equations ... as a tool to solve the initial-value problem for scalar, ...

It is seen as a great breakthrough in the research field of singular stochastic partial differential equations. "Up to then," Tempelmayr explains, "it was something of a mystery how to solve these ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...