This study makes the first attempt to apply the Kansa method in the solution of the time fractional diffusion equations, in which the MultiQuadrics and thin plate spline serve as the radial basis function. In the discretization formulation, the finite difference scheme and the Kansa method are respectively used to discretize time fractional derivative and spatial derivative terms. The numerical...

In this paper, we use Kansa method for solving the system of differential equations in the area of biology. One of the challenges in Kansa method is picking out an optimum value for Shape parameter in Radial basis function to achieve the best result of the method because there are not any available analytical approaches for obtaining optimum Shape parameter. For this reason, we design a genetic...

Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...

This paper formulates a simple explicit local version of the classical meshless radial basis function collocation (Kansa) method. The formulation copes with the diffusion equation, applicable in the solution of a broad spectrum of scientific and engineering problems. The method is structured on multiquadrics radial basis functions. Instead of global, the collocation is made locally over a set o...

Solving partial diierential equations by collocation with radial basis functions can be eeciently done by a technique rst proposed by E. Kansa in 1990. It rewrites the problem as a generalized interpolation problem, and the solution is obtained by solving a (possibly large) linear system. The method has been used successfully in a variety of applications, but a proof of nonsingularity of the li...