In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

This paper formulates a local Radial Basis Functions (LRBFs) collocation method for the numerical solution of the non-linear dispersive and dissipative KdV-Burger’s (KdVB) equation. This equation models physical problems, such as irrotational incompressible flow, considering a shallow layer of an inviscid fluid moving under the influence of gravity and the motion of solitary waves. The local ty...

Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions (r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain \Kriging function", which allows a formulation as an integral involving the Fourier transform of. The explicit construction of locally well{behaving adm...

abstract Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientiic visualization. We introduce geometric uncertainty as a measure of interpolation error, level of conndence or quality of an interpolant. Geometric uncertainty can be estimated as a scalar or a vector-valued function that depends upon ge...

Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only non-oscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as their limiting case) leads to non-singular interpolants with in...

Sampling inequalities give a precise formulation of the fact that a differentiable function cannot attain large values, if its derivatives are bounded and if it is small on a sufficiently dense discrete set. Sampling inequalities can be applied to the difference of a function and its reconstruction in order to obtain (sometimes optimal) convergence orders for very general possibly regularized r...

Interpolation by analytic radial basis functions like the Gaussian and inverse multiquadrics can degenerate in two ways: the radial basis functions can be scaled to become “increasingly flat”, or the data points “coalesce” in the limit while the radial basis functions stays fixed. Both cases call for a careful regularization. If carried out explicitly, this yields a preconditioning technique fo...

This article pertains to interpolation of Sobolev functions at shrinking lattices hZ from Lp shift-invariant spaces associated with cardinal functions related to general multiquadrics, φα,c(x) := (|x| + c). The relation between the shift-invariant spaces generated by the cardinal functions and those generated by the multiquadrics themselves is considered. Additionally, Lp error estimates in ter...