TY - JOUR
T1 - Implicit Finite Difference Scheme for Singularly Perturbed Burger-Huxley Equations
AU - Jima Kabeto , Masho
AU - Duressa , Gemechis File
JO - Journal of Partial Differential Equations
VL - 1
SP - 87
EP - 100
PY - 2021
DA - 2021/10
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/19911.html
KW - Singularly perturbed, Burger-Huxley equation, higher-order, accurate solution.
AB - <p style="text-align: justify;">In this paper, an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation. The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation. The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique. This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration. The derivatives are replaced by finite difference approximation, then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction. The convergence analysis of the proposed method has been established. Numerical experiments were conducted to support the theoretical results. Further, the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.</p>