Solitary wave solutions for a coupled pair of mKdV equations

Propagation of weakly nonlinear long waves is studied within the framework of a system of two coupled modified Korteweg-de Vries equations. We investigate analytically and numerically the various families of soliton states for the considered model. By scaling the functions and variables we find that the resulting coupled pair of equations has only one combined parameter. This parameter depends on the wave speed and the coupling coefficient. Explicit analytical expressions for both of the symmetric and antisymmetric states are determined. Numerical method is derived to solve the proposed system, many numerical tests have been conducted to study the behavior of the solution, and the existence of the asymmetric soliton states is displayed numerically.     

Two-time level ADI finite volume method for a class of second-order hyperbolic problems

In this paper, we develop a two-time level alternating direction implicit (ADI) method for a class of second-order hyperbolic problems on a rectangular domain. The method builds on the finite volume method with biquadratic basis functions for the discretization in space, and a Crank-Nicolson approach for the time stepping. We obtain a second-order error estimation in the H¹ norm. Numerical experiments are performed to demonstrate the theoretical findings.     

ESTIMATOR COMPETITION FOR POISSON PROBLEMS

We compare 13 different a posteriori error estimators for the Poisson problem with lowest-order finite element discretization. Residual-based error estimators compete with a wide range of averaging estimators and estimators based on local problems. Among our five benchmark problems we also look on two examples with discontinuous isotropic diffusion and their impact on the performance of the estimators. （Supported by DFG Research Center MATHEON.）     

A class of methods for diffusion-convection equations

A class of method with a free parameter(s) is considered for the solution of the diffusion–convection equation. This class is obtained using interpolation function approach and so, some classic methods appears when s take specific values. In order to obtain a non–oscillatory numerical solution some restrictions will be placed on s. Choosing two suitable methods of that class, an algorithm will be established and computational requirements will be considered     

The Structure of Finite Non-Nilpotent Groups in Which Every 2-Maximal Subgroup Permutes with all 3-Maximal Subgroups

The structure of finite non-nilpotent groups in which every 2-maximal subgroup permutes with every 3-maximal subgroup is described.     

On Central Automorphisms Fixing the Center Element-Wise

Let G be a finite p-group of nilpotency class 2. We find necessary and sufficient conditions on G such that each central automorphism of G fixes the center of G element-wise.     

Subgroups of a Direct Product of Groups that Satisfy the Strong Frattini Argument

We give criteria to characterize subgroups of a direct product of finite solvable groups that satisfy the strong Frattini argument.     

On the Construction of Finite Oscillator Dictionary

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in [3 Gurevich , S. , Hadani , R. , Sochen , N. (2008). The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. Inform. Theory 54(9):4239–4253.[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, closed formulae of the finite split oscillator dictionary 𝔖 ^s are revisited by a simple proof, the structure of nonsplit tori of the group SL(2, 𝔽 _p ) is studied, and an explicit algorithm for computing the finite nonsplit oscillator dictionary 𝔖 ^ns is described.     

Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains

In two-dimensional Euclidean space, a simply connected unbounded domain whose boundary is a Jordan curve is called an unbounded Jordan domain. In this article, we discuss a piecewise linear finite element approximation of conformal mappings from the unit disk of the plane to unbounded Jordan domains. Some convergence results and error analysis are presented. Numerical examples are also given.