Improvement of numerical solution of selfadjoint singular perturbation problems by incorporation of asymptotic approximations

摘要

A numerical method for singularly perturbed two-point boundary-value problems for second-order ordinary differential equations without a first derivative term arising in the study of chemical catalysis and Michaelis-Menten process in biology is proposed. In this method (“Booster method”), an asymptotic approximation is incorporated into a suitable finite-difference scheme to improve the numerical solution. Uniform error estimates are derived for this method when implemented in known difference schemes. An improvement by a factor of ɛn+1 can be obtained (where ɛ is the small parameter and n is the order of the asymptotic approximation) for a small amount of extra work. Numerical results are presented in support of this claim.