In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization of partial differential equations (PDEs). We tested the effectiveness of the algorithm on several PDEs using different number of sub-domains (ranging from 8...

The main purpose of this work is to present a new double transform called the ARA-Sumudu (DARA-ST). application some basic functions and master properties are introduced. convolution existence theorems also presented proved. These results implemented obtain solution partial differential equations (PDEs), integral (IEs) functional equations. We formulas for solving families PDEs. latter ones use...

A variational formulation of a general form fourth order geometric partial differential equation is derived, and based on which a mixed finite element method is developed. Several surface modeling problems, including surface blending, hole filling and surface mesh refinement with the G continuity, are taken into account. The used geometric partial differential equation is universal, containing ...

This document describes a toolbox of level set methods for solving time-dependent Hamilton-Jacobi partial differential equations (PDEs) in the Matlab programming environment. Level set methods are often used for simulation of dynamic implicit surfaces in graphics, fluid and combustion simulation, image processing, and computer vision. Hamilton-Jacobi and related PDEs arise in fields such as con...

The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs have appeared long time ago, both as the equations for the adjoint process in stochastic control, as ...

Abstract In this paper, we concentrate on the Lie symmetry structure of a system multi-dimensional time-fractional partial differential equations (PDEs). Specifically, first give an explicit prolongation formula involving Riemann–Liouville derivative for infinitesimal generator in case, and then show that has elegant structure. Furthermore, present two simple conditions to determine generators ...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

2-D convection-diffusion, reacting flows in a single channel of catalytic monoliths are investigated. The fluid dynamics are modelled by a steady state, boundary-layer equations, which is a large system of parabolic partial differential equations (PDEs) with nonlinear boundary conditions arising from the coupling between the gas-phase and surface processes. The chemical processes are modelled u...

This paper describes a concise specification language for linear partial differential equations (PDEs) on a union of rectangles, along with three tools: a pretty-printer, TEX generator, and a code generator. The prettyprinter and TEX generator help users by allowing equations to be specified (and read) in their natural form, while the code generator allows implementors to separate their numeric...

We review an emerging application field to parabolic partial differential equations (PDEs), that’s economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic application of the maximum principle to the latter leads to single out a serious illpo...