In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

Radial basis function (RBF) methods have shown the potential to be a universal grid free method for the numerical solution of partial differential equations. Both global and compactly supported basis functions may be used in the methods to achieve a higher order of accuracy. In this paper, we take advantage of the grid free property of the methods and use an adaptive algorithm to choose the loc...

Abstract In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear have solutions that entail strong discontinuities and shocks, which give rise to numerical instabilities when solution is approximated by a We introduce residual-based artificial viscosity (RV) stabilization framework adjusted RBF-FD method, where r...

Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. This thesis employs a recently dev...

In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reaction-diffusion equation. A computational approach based on finite difference and RBF-collocation methods is conducted to solve the equation with respect to the appropriate initial and boundary conditions. The ability and robust...

The Burgers’ equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two d...

Burgers’ equations is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers’ equation numerically using the finite difference and collocation methods. After the temporal discretization of the equation using C-N Scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical result...

This paper made some significant advances in the dual reciprocity and boundary-only RBF techniques. The proposed boundary knot method (BKM) is different from the standard boundary element method in a number of important aspects. Namely, it is truly meshless, exponential convergence, integration-free (of course, no singular integration), boundary-only for general problems, and leads to symmetric...

This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...