Method of lines for multi-dimensional coupled viscous Burgers’ equations via nodal Jacobi spectral collocation method

2021 ◽  
Author(s):  
Bashar Zogheib ◽  
Emran Tohidi ◽  
Haci Mehmet Baskonus ◽  
Carlo Cattani
Keyword(s):  
Collocation Method ◽  
Method Of Lines ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Jacobi Spectral Collocation Method

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

scholarly journals Space–Time Spectral Collocation Method for Solving Burgers Equations with the Convergence Analysis

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1439 ◽  
Author(s):  
Yu Huang ◽  
Mohammad Hadi Noori Skandari ◽  
Fatemeh Mohammadizadeh ◽  
Hojjat Ahsani Tehrani ◽  
Svetlin Georgiev Georgiev ◽  
...  
Keyword(s):  
Collocation Method ◽  
Numerical Approach ◽  
Space Time ◽  
Dirichlet Boundary Conditions ◽  
Spectral Collocation Method ◽  
Test Problems ◽  
Algebraic Equations ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Chebyshev Spectral Collocation

This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation are first approximated by interpolating polynomials and then discretized at the Chebyshev–Gauss–Lobatto points. Thus, we get a system of algebraic equations whose solution is the set of unknown coefficients of the approximate solution of the main problem. We investigate the convergence of the suggested numerical scheme and compare the proposed method with several recent approaches through examining some test problems.

Sign in / Sign up

Export Citation Format

Share Document