SIAM Journal on Numerical Analysis, Vol. 46, No. 5 (2008), pp. 2411-2442 (32 pages) This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial ...

A superexponentially convergent method for solving the Sturm-Liouville problem with Legendre's differential operator is given. The presented method (called the FD-method) is based on the coefficient ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...

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 ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...