Symplectic multiquadric quasi-interpolation approximations of KdV equation

Applying Multiquadric Quasi-Interpolation to Solve KdV Equation

Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations. Based on the good performance, Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation, which is generalized from the LD operator, and used it to solve hyperbolic conservation laws and Burgers’...

Using multiquadric quasi-interpolation for solving Kawahara equation

Solving partial differential equation by using multiquadric quasi-interpolation

In this paper, we use a kind of univariate multiquadric (MQ) quasi-interpolation to solve partial differential equation (PDE). We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the r...

using multiquadric quasi-interpolation for solving kawahara equation

A New Approach to Improved Multiquadric Quasi-Interpolation by Using General Hermite Interpolation

Abstract In this paper, a new approach to improve univariate multiquadric operators is surveyed. The presented scheme is obtained by using Hermite interpolating polynomials where the function is approximated by generalized LB quasi-interpolation operator. Error analysis shows that the convergence rate depends on the shape parameter c. Thus, our operators could provide the desired smoothness and...