Application of differential quadrature to transport processes.

*(English)*Zbl 0538.65084The method of differential quadrature (DQ) is the alternative for the solution of partial differential equations to the conventional finite element and finite difference method. Briefly, the DQ method entails replacing each space partial derivative by a weighted linear sum of values of the function which is to be found. The DQ method is carefully and neatly demonstrated in the paper, namely, the corresponding numerical results and the exact ones for both 1D steady-state and transient-state transport equations are compared.

The conclusion is made in the paper that because of the reduction in programming effort and computational time, the technique of DQ appears to enjoy substantial advantages over the conventional finite element and finite difference methods for solving problems related to transport phenomena.

The conclusion is made in the paper that because of the reduction in programming effort and computational time, the technique of DQ appears to enjoy substantial advantages over the conventional finite element and finite difference methods for solving problems related to transport phenomena.

Reviewer: J.Smid

##### MSC:

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |

##### Keywords:

transport processes; convection-diffusion problem; comparison of methods; finite element method; method of differential quadrature
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\textit{F. Civan} and \textit{C. M. Sliepcevich}, J. Math. Anal. Appl. 93, 206--221 (1983; Zbl 0538.65084)

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##### References:

[1] | Bellman, R.E; Casti, J, Differential quadrature and long-term integration, J. math. anal appl., 34, 235-238, (1971) · Zbl 0236.65020 |

[2] | Bellman, R.E; Kashef, B.G; Casti, J, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, J. comput. phys., 10, 40-52, (1972) · Zbl 0247.65061 |

[3] | Bellman, R.E, (), Chap. 16 |

[4] | Bellman, R.E; Kashef, B.G, Solution of the partial differential equation of the hodgkins-Huxley model using differential quadrature, Math. biosci., 19, 1-8, (1974) · Zbl 0273.65088 |

[5] | Bellman, R.E; Roth, R.S, System identification with partial information, J. math. anal. appl., 68, 321-333, (1979) · Zbl 0427.93016 |

[6] | Bellman, R.E; Roth, R.S, A scanning technique for systems identification, J. math. anal. appl., 71, 403-411, (1979) · Zbl 0419.93023 |

[7] | Carslaw, H.S; Jaeger, J.C, Conduction of heat in solids, (1959), Oxford Univ. Press London · Zbl 0029.37801 |

[8] | Civan, F, Solution of transport phenomena type models by the method of differential quadratures, () |

[9] | \scF. Civan and C. M. Sliepcevich, “Differential quadrature for multidimensional problems,” to appear. · Zbl 0557.65084 |

[10] | Fehlberg, E, Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems, Nasa tr r-315, (July 1969) |

[11] | Forsythe, G.E; Moler, C.B, Computer solution of linear algebraic systems, (1967), Prentice-Hall Englewood Cliffs, N. J · Zbl 0154.40401 |

[12] | Mingle, J.O, Computational considerations in nonlinear diffusion, Internat. J. numer. methods engrg., 7, 103-116, (1973) · Zbl 0263.65102 |

[13] | Mingle, J.O, The method of differential quadrature for transient nonlinear diffusion, J. math. anal. appl., 60, 559-569, (1977) · Zbl 0372.65049 |

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