A. Ramesh Babu | Searcharxiv

arXiv2021

A SDFEM for system of two singularly perturbed problems of convection-diffusion type with discontinuous source term

We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit boundary layers as well as weak interior layers. A numerical method based on finite element method (Shishkin and Bakhvalov-Shishkin meshes) is presented. We derive an error estimate of order $O(N^{-1}\ln^{3/2}{N})$ in the energy norm with respect to the perturbation parameter. Numerical experiments are also presented to support our theoretical results.

math.NA↗

arXiv2019

Embedding Complete Multipartite Graphs into Certain Trees

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper, we embed complete multipartite graphs into certain trees, such as $k$-rooted complete binary trees and $k$-rooted sibling trees.

math.CO↗