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Modified Laguerre collocation method for solving 1‐dimensional parabolic convection‐diffusion problems
Author(s) -
Gürbüz Burcu,
Sezer Mehmet
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4721
Subject(s) - laguerre polynomials , mathematics , laguerre's method , collocation (remote sensing) , orthogonal collocation , collocation method , matrix (chemical analysis) , mathematical analysis , convection–diffusion equation , residual , method of mean weighted residuals , algorithm , finite element method , differential equation , orthogonal polynomials , galerkin method , computer science , classical orthogonal polynomials , ordinary differential equation , materials science , physics , machine learning , composite material , thermodynamics
In this study, we propose a modified Laguerre collocation method based on operational matrix technique to solve 1‐dimensional parabolic convection‐diffusion problems arising in applied sciences. The method transforms the equation and mixed conditions of problem into a matrix equation with unknown Laguerre coefficients by means of collocation points and operational matrices. The solution of this matrix equation yields the Laguerre coefficients of the solution function. Thereby, the approximate solution is obtained in the truncated Laguerre series form. Also, to illustrate the usefulness and applicability of the method, we apply it to a test problem together with residual error estimation and compare the results with existing ones. Besides, the algorithm of the present method is given to represent the calculation of approximate solution.