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 ...

Drichlet conditions specify the values of the dependent variables of the boundary points. Neumann conditions specify the values of the normal gradients of the boundary. Robin conditions defines a ...

Taiwanese Journal of Mathematics, Vol. 14, No. 6 (December 2010), pp. 2365-2381 (17 pages) The main purpose of the paper is to prove the existence, uniqueness and smoothness with respect to time ...

Abstract: This paper considers the initial-boundary value problem for the heat equation with a dynamic-type boundary condition. Under some regularity, consistency and orthogonality conditions, the ...

ABSTRACT: In this work, a conceptual numerical solution of the two-dimensional wave partial differential equation (PDE) is developed by coupling the Complex Variable Boundary Element Method (CVBEM) ...

Abstract: We study initial boundary value problems for linear scalar evolution partial differential equations, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 x L}. We show ...

Boundary value problems for nonlinear partial differential equations form a cornerstone of modern mathematical analysis, bridging theoretical advancements and practical real-world applications. These ...

PINNs are coordinate networks trained to be the solution to an initial-boundary value problem. The optimization problem is based on minimizing the residuum of the PDE in the domain, as well as ...