Turkish Journal of Mathematics
An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems
This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.
Singular perturbation problems, reaction-diffusion equations, asymptotic approximations, boundary layers, finite difference method
CENGİZCİ, SÜLEYMAN; NATESAN, SRINIVASAN; and ATAY, MEHMET TARIK
"An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 37.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/37