Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions. The key is to estimate directly the solution bounds in the H²-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence and optimal error estimates, respectively, of the proposed fully discrete schemes.

     

Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Journal of Optimization Theory and Applications - This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to...     

Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill. Moreover, a new algorithm is proposed with the aid of the simplified Hirota method, the conjugated parameters assignment and long wave limit strategies, from which multiwave interaction solutions among solitons, breathers and lump waves are generated.     

Meta-analysis on thermo-migration of tiny/nano-sized particles in the motion of various fluids

The importance of thermophoresis and its essential role in particle migration have led to many published reports (i.e. aim and objectives). However, there exists no report on thermo-migration of tiny/nano-sized particles in the motion of various fluids. A meta-analysis on the significance of either nano or tiny particles exposed to thermophoretic force owing to temperature gradient during the dynamics of liquid substances is deliberated upon in this report. The method of slope linear regression through the data point was adopted to scrutinize sixty (60) published reports in which the effects of thermophoresis (thermodiffusion) is deliberated upon. The outcome of the study shows that different responses to the force of a temperature gradient are sufficient enough to enhance the temperature distribution and the concentration of non-Newtonian fluid due to an increase in thermophoresis. Thermophoretic effect increases the concentration of fluids in which the relationship between the shear stress and shear strain is non-linear. Skin friction coefficients is a decreasing function of thermophoresis. Increase in thermophoretic deposition is achievable due to an increase in thermophoresis. The effect of haphazard motion of nanoparticles should be investigated when it increases negligibly and considerably large. Thermal radiation strongly influences the significance of thermo-migration of tiny particles on fluid flow.     

A multigrid method for the ground state solution of Bose–Einstein condensates based on Newton iteration

BIT Numerical Mathematics - In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose–Einstein condensates based on Newton iteration scheme. Instead of...