A numerical technique for solving nonlinear singularly perturbed delay differential equations

• Published in: Mathematical modelling and analysis Vol. 23; no. 1; pp. 64 - 78
• Main Authors: Kanth, A.S.V. Ravi, P. Murali, Mohan Kumar
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2018
• Subjects: Delay; Delay equations (Differential equations); Differential equations; Mathematical analysis; Mathematical research; nonlinear delay problems; Nonlinear differential equations; parametric cubic spline; Perturbation theory; quasilinearization; Sequences (Mathematics); singularly perturbed problems; parametric cubic spline; quasilinearization; nonlinear delay problems; singularly perturbed problems
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2018.005

This paper presents a numerical technique for solving nonlinear singularly perturbed delay differential equations. Quasilinearization technique is applied to convert the nonlinear singularly perturbed delay differential equation into a sequence of linear singularly perturbed delay differential equations. An exponentially fitted spline method is presented for solving sequence of linear singularly perturbed delay differential equations. Error estimates of the method is discussed. Numerical examples are solved to show the applicability and efficiency of the proposed scheme.