Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

A mathematician has developed new methods for the numerical solution of ordinary differential equations. These so-called multirate methods are highly efficient for large systems, where some components ...

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem y' = Ay are inside this region, the numerical ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients.

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 ...