Abstract—Partial integro-differential equations occur in many fields of science and engineering. Besides, the class of parabolic-type differential equations is modelled in compression of poro-viscoelastic media, reaction-diffusion problems and nuclear reactor dynamics. In recent years, most mathematical models used in many problems of physics, biology, chemistry and engineering are based on integral and integro-differential equations. In this work, we propose a new effective numerical scheme based on the Laguerre matrix-collocation method to obtain the approximate solution of one dimensional parabolic-type Volterra partial integro-differential equations with the initial and boundary conditions. The presented method reduces the solution of the mentioned partial integro-differential equation to the solution of a matrix equation corresponding to system of algebraic equations with unknown Laguerre coefficients. Also, some numerical examples together with error estimation are presented to illustrate the validity and applicability of the proposed scheme.

Index Terms—Laguerre series, laguerre matrix-collocation method, parabolic-type volterra partial integro-differential equations, error estimation.

The authors are with Department of Mathematics, Faculty of Art and Science, Celal Bayar University, 45140, Manisa, Turkey (email: burcugrbz@gmail.com).

Cite: Burcu Gürbüz, Mehmet Sezer, "A Numerical Solution of Parabolic-Type Volterra Partial Integro-differential Equations by Laguerre Collocation Method," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 49-58, 2017.