Boundary value problems for the diffusion equation with piecewise continuous time delay

Boundary Value Problems for the Diffusion Equation with Piecewise Continuous Time Delay

A study is made of partial differential equations with piecewise constant arguments. ’Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded type; and most importantly, an equation of neutral type (that is, including the derivative at different values oftime t).

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

A hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

Boundary-Value Problems for the Diffusion Equation in Domains with Disconnected Boundary

1. Introduction It is well known that diffusion of particles outside the trapping regions is germane to many problems in different divisions of physics and chemistry. Note also that mathematically similar problems arise in Stokes hydrodynamics, acoustics, heat transfer and electrostatics. The aim of the present paper is an attempt to give a comprehensive analysis of the different analytical app...