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

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 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 ...

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 ...

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 ...

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 ...

This article analyzes the existence and approximation of solutions to initial value problems for nonlinear fractional differential equations of arbitrary order. Several new approaches are furnished in ...

Researchers from The University of New Mexico and Los Alamos National Laboratory have developed a novel computational ...

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