A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆^(2) ± λ^(2)

查看全文 作　　者：Guangming [1]Yao;[1]C.S.Chen;Chia Cheng [2]Tsai 机构地区：[1]Department of Mathematics,University of Southern Mississippi,Hattiesburg,MS 39406,USA;[2]Department of Marine Environment Engineering,National Kaohsiung Marine University,Taiwan,China 出　　处：《Advances in Applied Mathematics and Mechanics》索引2009年第1卷第6期,共19页 摘　　要：In this paper,we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆^(2) ± λ^(2).Similar to the derivation of fundamental solutions,it is non-trivial to derive particular solutions for higher order differential operators.In this paper,we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D.The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration.Three numerical examples in both 2D and 3D are given to validate particular solutions we derived. 关 键 词：The method of fundamental solutions radial basis functions meshless methods polyharmonic splines the method of particular solutions