The use of generalized Laguerre functions for solving the equation of magnetohydydinamic flow due to a stretching cylinder. (English) Zbl 1369.35059
Summary: In this paper, we develop dual-Petrov-Galerkin approximations to linear third-order equation defined on unbounded domain. The convergence of proposed scheme is proved strictly. We also establish some basic results on generalized Laguerre orthogonal approximations. The nonlinear ordinary differential equation is solved using generalized Laguerre functions. Using the operational matrix of derivative, the problem is reduced to set of algebraic equations. We also present the comparison of this work with some other numerical results. It shows that the present solution is highly accurate.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
stretching cylinder; linear third-order equation; generalized Laguerre functions; operational matrix of derivative; dual-Petrov-Galerkin approximationsReferences:
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