A comparison of differential quadrature methods for the solution of partial differential equations. (English) Zbl 0781.65088
First of all the authors present a brief outline of the quadrature discretization method (QDM) as a generalization of standard spectral collocation methods. In fact they propose a discrete representation of the derivative operator for arbitrary subdivisions of the argument domain based on split range polynomial expansions. The state that split range QDM (SRQDM) may achieve the high accuracy and spectacular convergence rates of spectral methods and believe that these new schemes are capable of solving partial differential equations involving interior steep gradients and/or discontinuities.
Unfortunately their proof only consists of solving Burgers’ equation. At least for this equation SRQDM works well.
Unfortunately their proof only consists of solving Burgers’ equation. At least for this equation SRQDM works well.
Reviewer: C.I.Gheorghiu (Cluj-Napoca)
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
comparison; differential quadrature methods; quadrature discretization method; spectral collocation methods; split range polynomial expansions; convergence; Burgers’ equationReferences:
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