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.

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 ...