A uniform convergent method for singularly perturbed nonlinear differential-difference equation

Erkan Cimen, Gabil M. Amiraliyev

Abstract


In this paper, the singularly perturbed boundary-value problem for a
nonlinear second order delay differential equation is considered. For the numerical solution of this problem, we use an exponentially fitted
difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. Also, the method is first-order convergent in the discrete maximum norm uniformly in the perturbation parameter. Furthermore, numerical illustration provide support of the theoretical results.

Keywords


Singular perturbation; Boundary value problem; Fitted difference method; Delay differential equation; Uniform convergence

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DOI: http://dx.doi.org/10.26713%2Fjims.v9i1.565

eISSN 0975-5748; pISSN 0974-875X