S.Yu. Reutskiy1
CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 355-386, 2012, DOI:10.3970/cmes.2012.087.355
Abstract The paper presents a new meshless numerical technique for solving nonlinear Poisson-type equation ∇2u = f (x) + F(u,x) for x ∈ Rd, d =1,2,3. We assume that the nonlinear term can be represented as a linear combination of basis functions F(u,x) = ∑mMqmφm. We use the basis functions φm of three types: the the monomials, the trigonometric functions and the multiquadric radial basis functions. For basis functions φm of each kind there exist particular solutions of the equation ∇2ϕm = φm in an analytic form. This permits to write the approximate solution in the form uM = uf… More >
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