Improvement Of The Multiquadric Quasi-interpolation Lw2

Abstract

In this paper, we improve the multiquadric (MQ) quasi-interpolation operator 2 . The operator 2 is based on inverse multiquadric radial basis function (IMQ-RBF) interpolation, and Wu and Schaback's MQ quasi-interpolation operator . In definition process of the quasi-interpolation 2 , the second derivative of function is used that approximated by center finite difference. In this paper, we use compact finite difference for approximation of the second derivative and increase accuracy of quasi-interpolation 2 . Numerical experiments demonstrate that the proposed MQ quasi-interpolation scheme is valid.

Numerical Solution of the Nonlinear Klein-Gordon Equation Using Multiquadric Quasi-interpolation Scheme

“…Unfortunately, these meshless methods for time-dependent and time-independent partial differential equations require to solve ill-conditioned linear system [1, 18-20, 22-24, 26, 39]. So modified meshless schemes are developed, for instance, researchers [12,25,31,32,45] proposed the meshless schemes to solve Burgers' equation and KdV equation by using MQ quasi-interpolation without solving a large scale linear system. In [14], a numerical method is developed to solve sine-Gordon equation by using high accuracy MQ quasi-interpolant operator L W 2 without solving a linear system of equations at each time step.…”

Interval Interpolation By Newtons Divided Differences

“…Interval analysis play an important role in many fields, such as Fuzzy Theory, Statistics and Probability, Approximation theory, Game Theory and Computer Science; for examples see [1][2][3][4][5][6][7][8][9][10]. In this paper, we first present the real interval and their properties.…”