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M. A. Golberg, C. S. Chen and S. Karur, “Improved Multiquadric Apporoxmation for Partial Differential Equations,” Engineering Analysis with Boundary Elements, Vol. 18, No. 1, 1996, pp. 9-17. doi:10.1016/S0955-7997(96)00033-1

has been cited by the following article:

• TITLE: RBFs Meshless Method of Lines for the Numerical Solution of Time-Dependent Nonlinear Coupled Partial Differential Equations

  AUTHORS: Sirajul Haq, Arshad Hussain, Marjan Uddin

  KEYWORDS: RBFs, Meshless Method of Lines, Time-Dependent PDEs

  JOURNAL NAME: Applied Mathematics, Vol.2 No.4, March 31, 2011

  ABSTRACT: In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-difference and finite element methods to approximate spatial derivatives, this new technique does not require a mesh in the problem domain, and a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions. Accuracy of the method is assessed in terms of the error norms L2, L∞ and the three invariants C1, C2, C3. Numerical experiments are performed to demonstrate the accuracy and easy implementation of this method for the three classes of time-dependent nonlinear coupled partial differential equations.