A Taylor–Chebyshev approximation technique to solve the 1D and 2D nonlinear Burgers equations

2021 ◽  
Author(s):  
Mohammad Izadi ◽  
Şuayip Yüzbaşı ◽  
Dumitru Baleanu
Keyword(s):  
Chebyshev Approximation ◽  
Approximation Technique ◽  
Burgers Equations

scholarly journals Efficient RCS Computation Over a Broad Frequency Band Using Subdomain MoM and Chebyshev Approximation Technique

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 33522-33531
Author(s):  
Xing Wang ◽  
Haoxuan Gong ◽  
Shuai Zhang ◽  
Ying Liu ◽  
Ruipeng Yang ◽  
...  
Keyword(s):  
Frequency Band ◽  
Chebyshev Approximation ◽  
Approximation Technique ◽  
Broad Frequency Band

New cubic B-spline approximation technique for numerical solutions of coupled viscous Burgers equations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tahir Nazir ◽  
Muhammad Abbas ◽  
Muhammad Kashif Iqbal
Keyword(s):  
Numerical Solutions ◽  
Numerical Study ◽  
Spline Approximation ◽  
Current Approach ◽  
Superior Performance ◽  
Approximation Technique ◽  
Spatial Direction ◽  
Content Type ◽  
B Spline ◽  
Burgers Equations

Purpose The purpose of this paper is to present a new cubic B-spline (CBS) approximation technique for the numerical treatment of coupled viscous Burgers’ equations arising in the study of fluid dynamics, continuous stochastic processes, acoustic transmissions and aerofoil flow theory. Design/methodology/approach The system of partial differential equations is discretized in time direction using the finite difference formulation, and the new CBS approximations have been used to interpolate the solution curves in the spatial direction. The theoretical estimation of stability and uniform convergence of the proposed numerical algorithm has been derived rigorously. Findings A different scheme based on the new approximation in CBS functions is proposed which is quite different from the existing methods developed (Mittal and Jiwari, 2012; Mittal and Arora, 2011; Mittal and Tripathi, 2014; Raslan et al., 2017; Shallal et al., 2019). Some numerical examples are presented to validate the performance and accuracy of the proposed technique. The simulation results have guaranteed the superior performance of the presented algorithm over the existing numerical techniques on approximate solutions of coupled viscous Burgers’ equations. Originality/value The current approach based on new CBS approximations is novel for the numerical study of coupled Burgers’ equations, and as far as we are aware, it has never been used for this purpose before.

scholarly journals On the Analytical and Numerical Solutions of the Linear Damped NLSE for Modeling Dissipative Freak Waves and Breathers in Nonlinear and Dispersive Mediums: An Application to a Pair-Ion Plasma

2021 ◽  
Vol 9 ◽  
Author(s):  
S. A. El-Tantawy ◽  
Alvaro H. Salas ◽  
M. R. Alharthi
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Chebyshev Approximation ◽  
Rogue Waves ◽  
Approximation Technique ◽  
Damping Term ◽  
Analytical And Numerical Solutions ◽  
Ion Plasma ◽  
Finite Differences Method

In this work, two approaches are introduced to solve a linear damped nonlinear Schrödinger equation (NLSE) for modeling the dissipative rogue waves (DRWs) and dissipative breathers (DBs). The linear damped NLSE is considered a non-integrable differential equation. Thus, it does not support an explicit analytic solution until now, due to the presence of the linear damping term. Consequently, two accurate solutions will be derived and obtained in detail. The first solution is called a semi-analytical solution while the second is an approximate numerical solution. In the two solutions, the analytical solution of the standard NLSE (i.e., in the absence of the damping term) will be used as the initial solution to solve the linear damped NLSE. With respect to the approximate numerical solution, the moving boundary method (MBM) with the help of the finite differences method (FDM) will be devoted to achieve this purpose. The maximum residual (local and global) errors formula for the semi-analytical solution will be derived and obtained. The numerical values of both maximum residual local and global errors of the semi-analytical solution will be estimated using some physical data. Moreover, the error functions related to the local and global errors of the semi-analytical solution will be evaluated using the nonlinear polynomial based on the Chebyshev approximation technique. Furthermore, a comparison between the approximate analytical and numerical solutions will be carried out to check the accuracy of the two solutions. As a realistic application to some physical results; the obtained solutions will be used to investigate the characteristics of the dissipative rogue waves (DRWs) and dissipative breathers (DBs) in a collisional unmagnetized pair-ion plasma. Finally, this study helps us to interpret and understand the dynamic behavior of modulated structures in various plasma models, fluid mechanics, optical fiber, Bose-Einstein condensate, etc.

A Chebyshev Approximation Technique Based on AIM-PO for Wideband Analysis

2016 ◽  
Vol 15 ◽  
pp. 93-97 ◽  
Author(s):  
Xing Wang ◽  
Shuai Zhang ◽  
Hui Xue ◽  
Shu-Xi Gong ◽  
Zi-Liang Liu
Keyword(s):  
Chebyshev Approximation ◽  
Approximation Technique

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4380-4386
Author(s):  
Tu Xianping ◽  
Lei Xianqing ◽  
Ma Wensuo ◽  
Wang Xiaoyi ◽  
Hu Luqing ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Evaluation Method ◽  
Geometry Optimization ◽  
Reference Points ◽  
Approximation Technique ◽  
Error Evaluation ◽  
Iterative Approximation ◽  
Logarithmic Curve ◽  
Normal Distance ◽  
Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

scholarly journals Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

2021 ◽  
Author(s):  
Alessandro Barbiero ◽  
Asmerilda Hitaj
Keyword(s):  
Order Approximation ◽  
Linear Optimization ◽  
Closed Form Solution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Computation Time ◽  
Form Solution ◽  
Engineering Problem ◽  
Approximation Technique ◽  
Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

Treatment of Pediatric Sternotomy Wound Complications: A Minimally Invasive Approach

2021 ◽  
Author(s):  
Taehee Jo ◽  
Joon Hur ◽  
Eun Key Kim
Keyword(s):  
Negative Pressure Wound Therapy ◽  
Wound Dehiscence ◽  
Surgical Debridement ◽  
Wound Complications ◽  
Approximation Technique ◽  
Invasive Approach ◽  
Nonsurgical Management ◽  
Single Use ◽  
Sternal Wound Infections ◽  
Deep Sternal Wound Infections

Abstract Background Pediatric sternal wound complications (SWCs) include sterile wound dehiscence (SWD) and superficial/deep sternal wound infections (SSWI/DSWI), and are generally managed by repetitive debridement and surgical wound approximation. Here, we report a novel nonsurgical management strategy of pediatric sternotomy wound complications, using serial noninvasive wound approximation technique combined with single-use negative pressure wound therapy (PICO) device. Methods Nine children with SWCs were managed by serial approximation with adhesive skin tapes and serial PICO device application. Thorough surgical debridement or surgical approximations were not performed. Results Three patients were clinically diagnosed as SWD, two patients as SSWI, and four patients as DSWI. None of the wounds demonstrated apparent mediastinitis or bone destructions. PICO device was applied at 16.1 days (range: 6–26 days) postoperatively, together with serial wound approximation by skin tapes. The average duration of PICO use was 16.9 days (range: 11–29 days) and the wound approximation was achieved in all patients. None of the patients underwent aggressive surgical debridement or invasive surgical approximation by sutures. Conclusion We report our successful management of selected pediatric SWCs, using serial noninvasive wound approximation technique combined with PICO device.

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