Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Inspired by path integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids ...

For the initial value problem associated with second order advanced differential equation on Banach space, it is constructed a numerical method to approximate the solution. The method uses the ...

This is a preview. Log in through your library . Journal Information This journal, begun in 1943 as Mathematical Tables and Other Aids to Computation, publishes original articles on all aspects of ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

A Russian mathematician has developed a new method for analyzing a class of equations that underpin models in physics and ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...