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 ...

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

The course is devoted to analytical methods for partial differential equations of mathematical physics. Review of separation of variables. Laplace Equation: potential theory, eigenfunction expansions, ...

Taiwanese Journal of Mathematics, Vol. 10, No. 4 (June 2006), pp. 963-975 (13 pages) We apply the two-scale convergence method introduced by G. Nguetseng and G. Allaire to study the homogenization of ...