A New Computational Method Based on Laguerre Polynomials for Solving Certain Nonlinear Partial Integro Differential Equations

B. Gürbüz, M. Sezer Manisa Celal Bayar University, Department of Mathematics, Faculty of Science and Letters, Manisa, Turkey

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In this study, we consider some nonlinear partial integro-differential equations. Most of these equations are used as mathematical models in many problems of physics, biology, chemistry, engineering, and in other areas. Our main purpose is to propose a new numerical method based on the Laguerre and Taylor polynomials, called matrix collocation method, for the numerical solution of the mentioned nonlinear equations under the initial or boundary conditions. To show the effectiveness of this approach, some examples along with error estimations are illustrated by tables and figures.

DOI: 10.12693/APhysPolA.132.561 topics: nonlinear partial integro-differential equations, Laguerre polynomials, matrix and collocation methods, error estimations