An improvement of Laguerre computational scheme for solving nonlinear age-structured population models

Volume 19, Issue 4, pp 268--287 http://dx.doi.org/10.22436/jmcs.019.04.07

Publication Date: July 13, 2019 Submission Date: December 01, 2017 Revision Date: May 22, 2019 Accteptance Date: June 15, 2019

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Authors

Zakieh Avazzadeh - School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China. Mohammad Heydari - Department of Mathematics, Yazd University, P. O. Box: 89195-741, Yazd, Iran. Shantia Yarahmadian - Mississippi State University, MS 39762, United States.

Abstract

In this paper, we simultaneously implement two kinds of orthogonal polynomials for solving a nonlinear age-structured population model. This non-classic type of partial differential equation is typically defined in large domains that makes finding an accurate solution by common techniques to be difficult. The presented method namely modified generalized Laguerre-Chebyshev (MGLC), which is based on the modified generalized Laguerre functions and Chebyshev orthogonal polynomials provides the spectral accuracy. The theoretical and experimental analysis of the scheme reliability verifies the validity of the proposed method in large domains.

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Keywords

• Nonlinear age-structured population model
• generalized Laguerre functions
• modified generalized Laguerre functions
• orthogonal polynomials
• error analysis

MSC

•  35Q92
•  92D25
•  74S25
•  94A11

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