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Application of the multiquadric method for numerical solution of elliptic partial differential equations. (English) Zbl 0883.65083

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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J40 Boundary value problems for higher-order elliptic equations
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