A univariate quasi-multiquadric interpolationwith better smoothness

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’...

Univariate splines: Equivalence of moduli of smoothness and applications

Several results on equivalence of moduli of smoothness of univariate splines are obtained. For example, it is shown that, for any 1 ≤ k ≤ r+1, 0 ≤ m ≤ r − 1, and 1 ≤ p ≤ ∞, the inequality n−νωk−ν(s(ν), n−1)p ∼ ωk(s, n −1)p, 1 ≤ ν ≤ min{k,m + 1}, is satisfied, where s ∈ Cm[−1, 1] is a piecewise polynomial of degree ≤ r on a quasi-uniform (i.e., the ratio of lengths of the largest and the smalles...

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

using multiquadric quasi-interpolation for solving kawahara equation