Modified Laguerre collocation method for solving 1‐dimensional parabolic convection‐diffusion problems

• Published in: Mathematical methods in the applied sciences Vol. 41; no. 18; pp. 8481 - 8487
• Main Authors: Gürbüz, Burcu, Sezer, Mehmet
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 01.12.2018
• Subjects: algorithm; Collocation methods; Convection; convection‐diffusion equation; modified Laguerre collocation method; parabolic problem; residual error
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.4721

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.