The closed-form particular solutions for Laplace and biharmonic operators using a Gaussian function

Applied Mathematics Letters - Tập 46 - Trang 50-56 - 2015
A.R. Lamichhane1, C.S. Chen1
1Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS, USA

Tài liệu tham khảo

Partridge, 1992 Cheng, 2000, Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions, Eng. Anal. Bound. Elem., 24, 531, 10.1016/S0955-7997(00)00033-3 Muleshkov, 1999, Particular solutions of Helmholtz-type operators using higher order polyharmonic splines, Comput. Mech., 23, 411, 10.1007/s004660050420 Tsai, 2009, Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators, Eng. Anal. Bound. Elem., 33, 514, 10.1016/j.enganabound.2008.08.007 Chen, 2011, The method of particular solutions for solving elliptic problems with variable coefficients, Int. J. Numer. Methods Biomed. Eng., 8, 545 Chen, 2012, The method of particular solutions for solving certain partial differential equations, Numer. Methods Partial Differential Equations, 28, 506, 10.1002/num.20631 Yao, 2011, A localized approach for the method of approximate particular solutions, Comput. Math. Appl., 61, 2376, 10.1016/j.camwa.2011.02.007 Chen, 2008, The method of fundamental solutions for solving elliptic PDEs with variable coefficients, 75 Yee, 2001 McCourt, 2013, Using gaussian eigenfunctions to solve boundary value problems, Adv. Appl. Math. Mech., 5, 569, 10.4208/aamm.13-13S08 Golberg, 1998, The method of fundamental solutions for potential, Helmholtz and diffusion problems, 103 Arfken, 1985 Fasshauer, 2007, On choosing optimal shape parameters for RBF approximation, Numer. Algorithms, 45, 345, 10.1007/s11075-007-9072-8 Rippa, 1999, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comput. Math., 11, 193, 10.1023/A:1018975909870 Fu, 2013, Boundary particle method for Laplace transformed time fractional diffusion equations, Comput. Phys., 235, 52, 10.1016/j.jcp.2012.10.018 Sarler, 1998, Axisymmetric augmented thin plate splines, Eng. Anal. Bound. Elem., 21, 81, 10.1016/S0955-7997(98)00004-6 Sarler, 2006, Axisymmetric multiquadrics, Eng. Anal. Bound. Elem., 30, 137, 10.1016/j.enganabound.2005.10.003