Fuzzy differential equations (FDEs) extend classical differential equations by incorporating uncertainty through fuzzy numbers. This mathematical framework is particularly valuable for modelling ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Backward Stochastic Differential Equations (BSDEs) constitute a powerful framework where the solution is determined by a terminal condition and then propagated backwards in time. This innovative ...

We all know how differential equations are a crucial part of engineering design and analysis. We have some powerful software tools for this today. Well, here is what led up to our modern analysis ...

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

Introduction to differential equations with an emphasis on engineering applications. Topics include first-order equations, higher-order linear equations with constant coefficients, and systems of ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...