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Zbl 0883.65083
Sharan, Maithili; Kansa, E.J.; Gupta, Suman
Application of the multiquadric method for numerical solution of elliptic partial differential equations. (English)
[J] Appl. Math. Comput. 84, No.2-3, 275-302 (1997). ISSN 0096-3003

This paper uses the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering. Two-dimensional Laplace, Poisson, and biharmonic equations describing the various physical processes have been taken as the test examples. The agreement is found to be very good between the computed and exact solutions. The method also provides an excellent approximation with a curved boundary.
[I.N.Katz (St.Louis)]

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
35J05 Laplace equation, etc.
35J40 Higher order elliptic equations, boundary value problems

Keywords: Laplace equation; Poisson equation; multiquadric approximation; biharmonic equations; test examples

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