Solution of Singularly Perturbed Differential-Difference Equations with Mixed Shifts Using Galerkin Method with Exponential Fitting | Zendy

D. Kumara Swamy | Zendy; K. Phaneendra | Zendy; Y. N. Reddy | Zendy

Open Access

Solution of Singularly Perturbed Differential-Difference Equations with Mixed Shifts Using Galerkin Method with Exponential Fitting

Author(s) -

D. Kumara Swamy,

K. Phaneendra,

Y. N. Reddy

Publication year - 2016

Publication title -

chinese journal of mathematics

Language(s) - English

Resource type - Journals

ISSN - 2314-8071

DOI - 10.1155/2016/1935853

Subject(s) - galerkin method , mathematics , mathematical analysis , singular perturbation , convergence (economics) , method of matched asymptotic expansions , exponential function , tridiagonal matrix , differential equation , eigenvalues and eigenvectors , finite element method , physics , quantum mechanics , economics , thermodynamics , economic growth

Galerkin method is presented to solve singularly perturbed differential-difference equations with delay and advanced shifts using fitting factor. In the numerical treatment of such type of problems, Taylor’s approximation is used to tackle the terms containing small shifts. A fitting factor in the Galerkin scheme is introduced which takes care of the rapid changes that occur in the boundary layer. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the tridiagonal system of the fitted Galerkin method. The method is analysed for convergence. Several numerical examples are solved and compared to demonstrate the applicability of the method. Graphs are plotted for the solutions of these problems to illustrate the effect of small shifts on the boundary layer solution

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