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...

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

Choosing the scale or shape parameter of radial basis functions (RBFs) is a well-documented but still an open problem in kernel-based methods. It common to tune it according applications, and plays crucial role both for accuracy stability method. In this paper, we first devise direct relation between RBFs their curvature at each point. This leads characterizing scalable unscalable ones. We prov...