M.A. Golberg1, C.S. Chen2
CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 87-96, 2001, DOI:10.3970/cmes.2001.002.087
Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in Rd, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations by using polyharmonic spline… More >
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