TY - JOUR
ID - 6601
TI - A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay
JO - Journal of Mathematical Modeling
JA - JMM
LA - en
SN - 2345-394X
AU - Negero, Naol Tufa
AD - Department of Mathematics, Wollega University, Nekemte, Ethiopia
Y1 - 2023
PY - 2023
VL - 11
IS - 2
SP - 395
EP - 410
KW - Singular perturbation
KW - time-delayed parabolic convection-diffusion problems
KW - two small parameters
KW - the method of line
KW - finite difference scheme
KW - uniform convergence
DO - 10.22124/jmm.2023.23001.2039
N2 - This paper presents a parameter-uniform numerical scheme for the solution of two-parameter singularly perturbed parabolic convection-diffusion problems with a delay in time. The continuous problem is semi-discretized using the Crank-Nicolson finite difference method in the temporal direction. The resulting differential equation is then discretized on a uniform mesh using the fitted operator finite difference method of line scheme. The method is shown to be accurate in $ O(\left(\Delta t \right)^{2} + N^{-2}) $, where $ N $ is the number of mesh points in spatial discretization and $ \Delta t $ is the mesh length in temporal discretization. The parameter-uniform convergence of the method is shown by establishing the theoretical error bounds. Finally, the numerical results of the test problems validate the theoretical error bounds.
UR - https://jmm.guilan.ac.ir/article_6601.html
L1 - https://jmm.guilan.ac.ir/article_6601_796659fd522b120398d31fc34a7f5dd8.pdf
ER -