Open AccessUNIFORMLY-CONVERGENT NUMERICAL METHODS FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION–DIFFUSION EQUATIONS WITH MIXED TYPE BOUNDARY CONDITIONS
Author(s) -
R. Mythili Priyadharshini,
N. Ramanujam
Publication year - 2013
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2013.851629
Subject(s) - mathematics , ordinary differential equation , mathematical analysis , infimum and supremum , convection–diffusion equation , type (biology) , uniform convergence , boundary value problem , numerical analysis , norm (philosophy) , singular perturbation , convergence (economics) , uniform norm , differential equation , ecology , computer network , bandwidth (computing) , economic growth , computer science , political science , law , economics , biology
In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection - diffusion second order ordinary differential equations subject to the mixed type boundary conditions. We prove that the method has almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and also the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.