Analysis of soliton phenomena in (2+1)-dimensional Nizhnik-Novikov-Veselov model via a modified analytical technique

The present research applies an improved version of the modified Extended Direct Algebraic Method (mEDAM) called +mEDAM to examine soliton phenomena in a notable mathematical model, namely the (2+1)-dimensional Nizhnik-Novikov-Veselov Model (NNVM), which possesses potential applications in exponentially localized structure interactions. The generalized hyperbolic and trigonometric functions are used to disclose a variety of soliton solutions, including kinks, anti-kink, bell-shaped and periodic soliton. Some 3D graphs are plotted for visual representations of these solutions which highlight their adaptability. The results provide a basis for practical usage and expansions to related mathematical models or physical systems. They also expand our understanding of the NNVM's dynamics, providing insights into its behavior and prospective applications

Innovative approach for developing solitary wave solutions for the fractional modified partial differential equations

The current work investigates solitary wave solutions for the fractional modified Degasperis-Procesi equation and the fractional gas dynamics equation with Caputo's derivative by using a modified extended direct algebraic method. This method transforms the targeted fractional partial differential equations (FPDEs) into more manageable nonlinear ordinary differential equations, which are then turned into systems of nonlinear algebraic equations with a series-based solution assumption. Using Maple 13, the solitary wave solutions are then obtained by solving the obtained systems. The method produces multiple innovative solitary wave solutions for both equations, which are graphically depicted as 3D and 2D graphs and provide important insights into their behaviors. These insights help us to comprehend wave behavior and the physical processes represented by these equations. Furthermore, the suggested technique exhibits dependability and efficacy in dealing with complicated FPDEs, which bodes well for future studies on the subject

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described