Elliptic equations represent a fundamental class of partial differential equations that arise in numerous models of steady-state processes, ranging from heat conduction to elasticity. Their study ...

The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 (34 pages) The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Investigation is made into the sensitivity of solutions of linear boundary value problems to perturbations of the boundary condition. We derive a useful quantity to decide for well or ill conditioning ...