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 ...

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 ...

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, ...

Let Φ(z) = ∑∞ 0 βjz j have radius of convergence $r (0 < r < \infty)$ and no singularities other than poles on the circle |z| = r. A complete solution is ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...