Conservative modified Serre–Green–Naghdi equations with improved dispersion characteristics

Optimized Dispersion Characteristics of the Boussinesq Wave Equations

In this paper a new set of Boussinesq wave equations with improved linear dispersion properties is proposed for extending its application to deeper water without having its mathematical form changed. The improvements are due to the combination of a generalized set of Boussinesq wave equations expressed in terms of any velocity, with additional dispersive terms obtained by invoking the linear sh...

Conservative Front Tracking with Improved Accuracy

We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has O(∆x) errors, improving over O(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assert...

Near Scale Invariance with Modified Dispersion Relations

A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS

In this note, we propose a modification of Steffensen's method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.  

Improved Hessian approximation with modified secant equations for symmetric rank-one method

Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new a...