Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

• Autorzy: Sekar Elango , Tamilselvan Ayyadurai

Identyfikatory

DOI

10.17512/jamcm.2019.2.09

• Języki publikacji: EN

Abstrakty

EN

A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

Słowa kluczowe

EN

singular perturbation problem; finite difference scheme; delay; integral boundary condition; error estimate

PL

schemat różnic skończonych; opóźnienie; oszacowanie błędu; metoda numeryczna; metoda równań skończonych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 2
• Strony: 99--110
• Opis fizyczny: Bibliogr. 13 poz., rys., tab.

Twórcy

autor

Sekar Elango

• Bharathidasan University Tiruchirappalli, India

autor

Tamilselvan Ayyadurai

• Bharathidasan University Tiruchirappalli, India

Bibliografia

• [1] Amiraliyev, G.M., & Cimen, E. (2010). Numerical method for a singularly perturbed convectiondiffusion problem with delay. Applied Mathematics and Computation, 216, 2351-2359.
• [2] Cimen, E. (2018). Numerical solution of a boundary value problem including both delay and boundary layer. Mathematical Modeling and Analysis, 23(4), 568-581.
• [3] Cimen, E., & Cakir, M. (2018). Convergence analysis of finite difference method for singularly perturbed nonlocal differential-difference problem. Miskolc Mathematical Notes, 19(2), 795-812.
• [4] Mahendran, R., & Subburayan, V. (2018). Fitted finite difference method for third order singularly perturbed delay differential equations of convection diffusion type. International Journal of Computational Methods, 15(1).
• [5] Subburayan, V., & Ramanujam, N. (2014). An initial value method for singularly perturbed third order delay differential equations. Proc. Int. Conf. Mathematical Sciences, Sathyabhama University, Chennai, India, 221-229.
• [6] Sekar, E., & Tamilselvan, A. (2018). Singularly perturbed delay differential equations of convection diffusion type with integral boundary condition. Journal of Applied Mathematics and Computing, 1-22.
• [7] Choi, Y.S., &Chan, K.Y. (1992). A Parabolic equation with nonlocal boundary conditions arising from electrochemistry, Nonlinear Analysis, 18, 317-331.
• [8] Day,W.A. (1992). Parabolic equations and thermodynamics. Quarterly of Applied Mathematics, 50, 523-533.
• [9] Cannon, J. (1963). The solution of the heat equation subject to the specification of energy. Quarterly of Applied Mathematics, 21, 155-160.
• [10] Bahuguna, D., Abbas, S., & Dabas, J. (2008). Partial functional differential equation with an integral condition and applications to population dynamics. Nonlinear Analysis, 69, 2623-2635.
• [11] Bahuguna, D., & Dabas, J. (2008). Existence and uniqueness of a solution to a semilinear partial delay differential equation with an integral condition. Nonlinear Dynamics and Systems Theory, 8(1), 7-19.
• [12] Sekar, E., & Tamilselvan, A. (2019). Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition. Journal Applied Mathematics and Computing, 1-14.
• [13] Miller, J.J.H., O’Riordan, E., & Shishkin, G.I. (1996). Fitted Numerical Methods for Singular Perturbation Problems. Singapore, New Jersey, London, Hong Kong: World Scientific Publishing Co.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).