Numerical Solution for Kawahara Equation by Using Spectral Methods

AbstractSome nonlinear wave equations are more difficult to investigate mathematically, as no general analytical method for their solutions exists. The Exponential Time Differencing (ETD) technique requires minimum stages to obtain the requiredaccurateness, which suggests an efficient technique relatingto computational duration thatensures remarkable stability characteristicsupon resolving nonlinear wave equations. This article solves the diagonal example of Kawahara equation via the ETD Runge-Kutta 4 technique. Implementation of this technique is proposed by short Matlab programs

Ab–initio study of the electronic and optical traits of Na0.5Bi0.5TiO3 nanostructured thin film

The electronic, and optical properties of rhombohedral Na0.5Bi0.5TiO3nanostructured thin film have been studied by the first–principle approach. Densityfunctional theory (DFT) has been employed to calculate the fundamental properties ofthe layers using full–potential linearized augmented plane–wave (FPLAPW) method. A2×2×1 supercell was constructed with two vacuum slabs on top and down of thesupercell. A geometry optimization was performed by PBE method. The optimized thinfilm structure was used for the intended calculations. As well, the reflectance, dielectricfunction, refractive index, of the thin film were calculated in the UV–vis region. Resultsshowed very well consistency with the available experimental and theoretical reports.The optical conductivity also followed a similar trend to that of the dielectric constants.Energy loss function of the modeled compound was also evaluated. The evaluated lossfunction showed sharp peaks in UV-vis region and followed a steady state in IR, MIRand FIR parts of spectrum

A review for the time integration of semi-linear stiff problems

Several real-world requests that involve conditions where different physical phenomena perform on very different time scales arise simultaneously. The partial differential equations (PDEs) that manage such situations are classified as stiff PDEs. Stiffness is a difficult property of differential equations (DEs) that avoid conservative explicit numerical integrators from managing problem efficiency. There has also been a large compact of importance in the building of exponential integrators. However, different some of the new literature proposes, integrators based on this philosophy have been confirmed since at least 1960.The aim of this study is to review the time integration proposed for semi-linear stiff problems

Split-step multi-symplectic method for nonlinear schrödinger equation

Multi-symplectic methods have recently been cons idered as a generalization of symplectic ODE methods to the case of Hamiltonian PDEs. The symplectic of Hamiltonian systems is well known, but for Partial Differential Equation (PDEs) this is a global pr operty. In addition, many PDEs can be written as Multi- symplectic systems, in which each independent variable has a distinct symplectic structure. Also, Their excellent long time behavior for a variety of Hamiltoni an wave equations has been proposed in a number of numerical studies. In the study, a new type of multi-symlectic integrators, which is used for solving Nonlinear Schrödinger Equation (NLS) has been demonstrated

A numerical approach for solving a general nonlinear wave equation

An analysis of various numerical schemes and boundary conditions on a general nonlinear wave equation is considered in this study. In particular, the Lax-Wendroff, Leapfrog and Iterated Crank Nicholson methods with Dirichlet boundary conditions are used to solve this nonlinear wave equation. The computation of the solution is made via the reduction of the nonlinear wave equation to the two variable and three variable systems

Error concealment using joint multiple description lioyd-max quantization and network coding

Multiple Description Coding (MDC) is a useful source coding method for concealing error in lossy networks. Network coding (NC) permits intermediate nodes within a network to apply algebraic mathematic process on independent streams in transmitter and receiver. This paper attempts to protect data and conceal errors happen in the network by joining MDC and p-cycle NC. First, input data (image) is zero padded and downsampled to four subimages. Then Wavelet and Lloyd-max quantization is applied to subimages. Later, four compressed and coded descriptions are transmitted through network and p-cycle network coding is applied to them in the network. Any lost description can be recovered exactly at the receiver part. In this method, no feedback system is needed. Results show that in the fixed bit rate, the PSNR (Peak Signal to Noise Ratio) of our reconstructed image and also subjective evaluation is better than previous work. Furthermore, proposed method has high throughput compared to another work

Optimizing Material Removal Rate (MRR) in WEDMing Titanium Alloy (Ti6Al4V) Using the Taguchi Method

Abstract: Selection of optimal cutting parameters has always been a critical issue to achieve high-quality in the machining process. In this study Design of Experiment (DOE) method for selection of optimal cutting parameters during WEDM of titanium alloy (Ti6Al4V) is experimentally studied. Moreover, the behaviour of three control parameters such as Pulse ON Time (A), Pulse OFF Time (B) and Peak Current (C) on machining performance, including Material Removal Rate (MRR) and Surface Roughness (SR) is studied using Analysis of Variance (ANOVA). This study has been establishedasa second-order mathematical model based on the Response Surface Methodology (RSM). The experimental plan was based on the face cantered, Central Composite Design (CCD). The residual analysis and confirmation runs indicate that the proposed models could adequately describe the performance of the factors that are being investigated. The results are particularly useful for scientists and engineers to determine which subset of the process variable has the greatest influence on the process performance