Application of the Multiquadric Method for Numerical Solution of Elliptic Partial Differential Equations
نویسندگان
چکیده
We have used 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. 276 M. SHARAN ET AL.
منابع مشابه
A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method
In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.
متن کاملUsing Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...
متن کاملA method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملNumerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative
In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff distance between the exact solution and approximate solution tends to zero.
متن کامل