Numerical study for system of ODEs obtained from MHD flow past a permeable flat plate in a Darcian porous medium using Laguerre collocation method. (English) Zbl 1462.65158
Summary: In this article, we introduce a numerical solution for the system of ODEs which governs the problem of magnetohydrodynamic boundary layer flow and heat transfer past a permeable flat plate which embedded in a porous medium by using an efficient Laguerre collocation method. The controlling parameters which affect the dimensionless velocity are the Darcy number, the Reynolds number and the magnetic number, whereas, the radiation parameter and Peclet number are the emerging parameters on the dimensionless temperature. The influence of these parameters on both the dimensionless velocity and the dimensionless temperature are analyzed graphically. The proposed method is based on replacement of the unknown function by a truncated series of the well-known Laguerre expansion of functions. An approximate formula of the integer derivative is introduced. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with Laguerre coefficients. Verification of the numerical Laguerre collocation method is tested after introducing the comparison with the previously published results.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76S05 | Flows in porous media; filtration; seepage |
| 80A21 | Radiative heat transfer |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 41A30 | Approximation by other special function classes |
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