HIGHER-ORDER UNIFORMLY CONVERGENT METHOD FOR SINGULARLY PERTURBED
BURGER-HUXLEY EQUATIONS
- Masho Kabeto,
- Gemechis Duressa
Abstract
In this paper, a higher-order uniformly convergent finite difference
method 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 under consideration. An upwind finite difference
approximation is applied in the temporal direction, and a nonuniform
Shishkin mesh type is used in the spatial direction. To accelerate the
rate of convergence from first to second-order, the Richardson
extrapolation technique is applied. The convergence analysis of the
proposed method has been established. Finally, numerical experiments
were conducted to support the theoretical results. Further, the result
shows that the proposed method gives more accurate solution than some
existing methods in the literature.