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1	On the Shape Parameter of the MFS-MPS Scheme Lin, Guo-Hwa 23 August 2010 (has links) In this paper, we use the newly developed method of particular solution (MPS) and one-stage method of fundamental solution (MFS-MPS) for solving partial differential equation (PDE). In the 1-D Poisson equation, we prove the solution of MFS-MPS is converge to Spectral Collocation Method using Polynomial, and show that the numerical solution similar to those of using the method of particular solution (MPS), Kansa's method, and Spectral Collocation Method using Polynomial (SCMP). In 2-D, we also test these results for the Poisson equation and find the error behaviors. particular solution method of fundamental solution radial basis functions error estimate meshless method
2	Applications of recurrence relation Chuang, Ching-hui 26 June 2007 (has links) Sequences often occur in many branches of applied mathematics. Recurrence relation is a powerful tool to characterize and study sequences. Some commonly used methods for solving recurrence relations will be investigated. Many examples with applications in algorithm, combination, algebra, analysis, probability, etc, will be discussed. Finally, some well-known contest problems related to recurrence relations will be addressed. characteristic equation characteristic root constant coefficients conjugate root distinct root Fibonacci numbers general solution homogeneous method of annihilator linear method of binary number system method of change of variable method of divide-and-conquer relation method of generating function multiple root method of logarithmic transformation nonhomogeneous nonlinear operator partial-fraction decomposition particular solution recurrence relation recurrence sequences

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On the Shape Parameter of the MFS-MPS Scheme

Applications of recurrence relation