‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

The finite element method (FEM) is a domain technique of solving the underlying governing equation in the region. The solution obtained in the total region is ideal to study energy/defect interactions, but the extensive discretization demands vast computer resources. On the other hand, the potential savings in computation resources, due to a limited surface or boundary discretization, is the pr...

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

annihilation or reduction of each kind of noise blended in correct data signals is a field that has attracted many researchers. it is a fact that fuzzy theory presents full capability in this field. fuzzy filters are often strong in smoothing corrupted signals, whereas they have simple structures. in this paper, a new powerful yet simple fuzzy procedure is introduced for sharpness reduction in ...

This paper is the first in a series of three, which analyze an adaptive approximate approach for solving (n + 1 (-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this approach the unknown functions of (n + 1) variables are projected onto finite linear combinations of functions of just n variables. This paper shows how the coefficients o...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids has been developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the...