Open AccessFitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations
Author(s) -
Gemechis File Duressa,
Mesfin Mekuria Woldaregay
Publication year - 2021
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.53.2022.3638
Subject(s) - mathematics , discretization , parabolic partial differential equation , partial differential equation , convergence (economics) , mathematical analysis , ftcs scheme , delay differential equation , variable (mathematics) , differential equation , ordinary differential equation , differential algebraic equation , economics , economic growth
In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using im- plicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.