A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity

Using multiquadric quasi-interpolation for solving Kawahara 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’...

Monotonicity-Preserving Piecewise Rational Cubic Interpolation

An explicit representation of a C1 piecewise rational cubic spline has been developed, which can produce a monotonic interpolant to given monotonic data. The explicit representation is easily constructed, and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant is given.

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...

Monotonicity-Preserving Linear Multistep Methods

In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total variation bounded (TVB) property. In the analysis the multistep methods are considered in combination with suitable starting proc...