an:02021533
Zbl 1040.65066
Lin??, Torsten; Madden, Niall
An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations
EN
Comput. Methods Appl. Math. 3, No. 3, 417-423 (2003).
00102646
2003
j
65L10 65L12 65L70 34B05 34E15 65L50
reaction diffusion equations; systems; singular perturbation; Shishkin mesh; error bound; finite difference scheme; numerical examples
This paper deals with the following system of two coupled singularly perturbed equations
\[
-\varepsilon^2 u^{\prime\prime}_1+ a_{11}(x) u_1+ a_{12}(x) u_2= f(x),
\]
\[
-\mu^2 u^{\prime\prime}_2+ a_{21}(x) u_1+ a_{22}(x) u_2= f_1(x),
\]
for \(x\in (0,1)\), \(\varepsilon,\mu\)-small constants, subject to homogeneous Dirichlet boundary conditions. The aim of the present study is to improve the theoretical error bound to almost second order for the case \(0< \varepsilon= \mu\ll 1\). A finite difference scheme on the Shiskin mesh is presented. The results of two numerical examples are given.
Pavol Chocholat?? (Bratislava)