scholarly journals A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers’ equation

2020 ◽  
Vol 39 (2) ◽  
Author(s):  
Kejia Pan ◽  
Xiaoxin Wu ◽  
Xiaoqiang Yue ◽  
Runxin Ni
Keyword(s):  
Burgers Equation ◽  
Sixth Order ◽  
Tvd Method ◽  
Coupled Burgers Equation

Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation

2017 ◽  
Vol 72 (9) ◽  
pp. 789-793
Author(s):  
Bo Xue ◽  
Fang Li ◽  
Yihao Li ◽  
Mingming Sun
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Burgers Equation ◽  
Integrable Equation ◽  
Explicit Solutions ◽  
Spectral Problems ◽  
Coupled Burgers Equation

AbstractBased on the gauge transformation between the corresponding 3×3 matrix spectral problems, N-fold Darboux transformation for a coupled Burgers’ equation is constructed. Considering the N=1 case of the derived Darboux transformation, explicit solutions for the coupled Burgers’ equation are given and their figures are plotted. Moreover, conservation laws of this integrable equation are deduced.

scholarly journals On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers' Equation

2019 ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Adem Kilicman
Keyword(s):  
Laplace Transform ◽  
Burgers Equation ◽  
Decomposition Methods ◽  
Laplace Transforms ◽  
Existence Condition ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Coupled Burgers Equation

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

scholarly journals Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

2019 ◽  
Vol 4 (2) ◽  
pp. 523-534 ◽  
Author(s):  
Ali Kurt ◽  
Mehmet Şenol ◽  
Orkun Tasbozan ◽  
Mehar Chand
Keyword(s):  
Water Waves ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Approximate Solutions ◽  
Iteration Algorithm ◽  
Shallow Water Waves ◽  
Fractional Differential ◽  
Reliable Methods ◽  
Coupled Burgers Equation ◽  
Partial Fractional Differential Equations

AbstractIn this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

A quartic trigonometric tension b-spline algorithm for nonlinear partial differential equation system

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Özlem Ersoy Hepson
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Higher Order ◽  
Spline Collocation ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
B Splines ◽  
Coupled Burgers Equation

Purpose The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers’ equation. Design/methodology/approach The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree. Findings The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program. Originality/value There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers’ equation.

Sign in / Sign up

Export Citation Format

Share Document