Convergence of Three-Step Taylor Galerkin Finite Element Scheme Based Monotone Schwarz Iterative Method for Singularly Perturbed Differential-Difference Equation |
| |
Authors: | B V Rathish Kumar Sunil Kumar |
| |
Institution: | 1. Department of Mathematics and Statistics , Indian Institute of Technology Kanpur , Kanpur , India bvrk@iitk.ac.in;3. Department of Mathematics and Statistics , Indian Institute of Technology Kanpur , Kanpur , India |
| |
Abstract: | Monotone Schwarz iterative methods for parabolic partial differential equations are well known for their advantage of eliminating the search for an initial solution. In this article, we propose a monotone Schwarz iterative method for singularly perturbed parabolic retarded differential-difference equations based on a three-step Taylor Galerkin finite element scheme. The stability and ε-uniform convergence of the three-step Taylor Galerkin finite element method have been discussed. Further, by using maximum principle and induction hypothesis, the convergence of the proposed monotone Schwarz iterative method has been established. |
| |
Keywords: | Boundary layer Exponentially fitted splines Finite element method Mass-lumped Maximum principle Monotone Schwarz iterative method (MSIM) Singularly perturbed problems (SPP) Taylor Galerkin method |
|