Numerical solution for advection-diffusion equation using collocation based new radial basis function

Abstract EN

In the present paper, a composite radial basis function was developed by a combination between thin plate and logarithmic radial basis functions.

This radial basis function was developed to overcome the singularity appeared when the source and field points coincide.

In based new radial function, the thin plate function was used when evaluating diagonal elements of the matrix coefficients and the logarithmic function was used for evaluating the other elements.

The advantage of using this new radial basis function represented by overcoming singularity from the diagonal elements when thin plate radialbasis function is used.

The new function is a combination of both multiquadric and thin plate radial basis functions.

One- and two-dimensional test examples were solved and the present results were compared with the analytical results and gave a good agreement in different applicant in applied mechanics and neural network .

Keywords: Collocation techniques, thin plate radial basis function, logarithmic radial basis function, advection-diffusion equation.