论文信息 - THE MODIFIED DIFFERENTIAL QUADRATURES AND THEIR APPLICATIONS

THE MODIFIED DIFFERENTIAL QUADRATURES AND THEIR APPLICATIONS

Abstract In this paper, a number of modifications are instituted in implementing the quadrature method for solving chemical engineering problems with semi-infinite domains and/or steep gradients. This improvement in the curve-fitting ability of differential quadratures is achieved by adopting trial functions of forms other than the polynomials. Formal criteria are first developed (and proved) for the selection of proper function forms. If the trial functions are restricted to the products of polynomials and some auxiliary functions, explicit formulae are derived to facilitate the calculation of the corresponding modified quadrature coefficients. If, in addition, the grid points are chosen to be the zeros of an orthogonal polynomial, e.g. Jacobi, Laguerre and Hermite, further simplifications can be realized to promote the efficiency and accuracy of the computation procedure. The modified differential quadratures have been applied to various example problems. From the data we have collected so far, it can b...

Chuei-Tin Chang | Chii-Shang Tsai | Tien-Tsai Lin

[1] Leon Lapidus,et al. Studies in approximation methods—I: Splines and control via discrete dynamic programming , 1978 .

[2] R. Bellman,et al. DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS , 1972 .

[3] J. Villadsen,et al. Solution of differential equation models by polynomial approximation , 1978 .

[4] George Adomian,et al. Partial Differential Equations , 1987 .

[5] A. Nayfeh. Introduction To Perturbation Techniques , 1981 .

[6] Chuei-Tin Chang,et al. New insights in solving distributed system equations by the quadrature method—II. Numerical experiments , 1989 .

[7] M. Duduković,et al. A moving finite element collocation method for transient problems with steep gradients , 1984 .

[8] B. Finlayson. Nonlinear analysis in chemical engineering , 1980 .

[9] S. Churchill. Chapter 12 – Integral Boundary-Layer Solution for Laminar Flow along a Flat Plate , 1988 .

[10] B. Finlayson. The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[11] Chuei-Tin Chang,et al. New insights in solving distributed system equations by the quadrature method—I. Analysis , 1989 .

[12] Thomas W. Chapman,et al. Solution of boundary-layer transport problems by orthogonal collocation , 1981 .

[13] S. Churchill,et al. Viscous flows : the practical use of theory , 1988 .