On the numerical solution of the diffusion equation subject to the specification of mass

Abstract

A parallel algorithm is developed for the numerical solution of the diffusion equation u, = u,,, 0 < * < X, 0 < / < 7\ subject to u(x, 0) = / ( * ) , u x (X, t) = g(t) and the specification of mass f a u(x,t)dx = M(t), 0 < b < X.

A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications

“…In [57,58] the method of lines semi-discretization approach is used to transform the model partial differential equation with a nonlocal boundary condition into system of first-order linear ordinary differential equations, the solution of which satisfies a certain recurrence relation involving matrix exponential terms. A suitable rational approximant is used to approximate such exponentials leading to a stable algorithm that may be parallelized through a partial-fraction splitting technique.…”

Third Order Parallel Splitting Method for Nonhomogeneous Heat Equation with Integral Boundary Conditions

“…Different examples of related problems of parabolic equations have been taken into account by many authors [24,25,26]. Taj et al [27] proposed the numerical technique for the solution of PPDEs by utilizing FD scheme and Pade approximation.…”

A new numerical method for heat equation subject to integral specifications

“…Dehghan applied some finite-difference schemes [13,17] and a shifted Tau method [19] for solving similar problem. Cases of similar forms of those parabolic equations have been considered by various authors [8,9,21]. The purpose of the present article is to give a method of solving problem (1.1) under initial condition (1.2) and integral conditions (1.3) and (1.4) by using the Laplace transform technique.…”