Space–time Chebyshev spectral collocation method for nonlinear time‐fractional Burgers equations based on efficient basis functions

2020 ◽  
Author(s):  
Yu Huang ◽  
Fatemeh Mohammadi Zadeh ◽  
Mohammad Hadi Noori Skandari ◽  
Hojjat Ahsani Tehrani ◽  
Emran Tohidi
Keyword(s):  
Collocation Method ◽  
Space Time ◽  
Basis Functions ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Chebyshev Spectral Collocation ◽  
Chebyshev Spectral Collocation Method

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.

scholarly journals Chebyshev Spectral Collocation Method for Population Balance Equation in Crystallization

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 317
Author(s):  
Chunlei Ruan
Keyword(s):  
Collocation Method ◽  
Spectral Collocation Method ◽  
Population Balance Equation ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Size Dependent ◽  
Chebyshev Spectral Collocation ◽  
Diffusive Term ◽  
Dependent Growth ◽  
Chebyshev Spectral Collocation Method

The population balance equation (PBE) is the main governing equation for modeling dynamic crystallization behavior. In the view of mathematics, PBE is a convection–reaction equation whose strong hyperbolic property may challenge numerical methods. In order to weaken the hyperbolic property of PBE, a diffusive term was added in this work. Here, the Chebyshev spectral collocation method was introduced to solve the PBE and to achieve accurate crystal size distribution (CSD). Three numerical examples are presented, namely size-independent growth, size-dependent growth in a batch process, and with nucleation, and size-dependent growth in a continuous process. Through comparing the results with the numerical results obtained via the second-order upwind method and the HR-van method, the high accuracy of Chebyshev spectral collocation method was proven. Moreover, the diffusive term is also discussed in three numerical examples. The results show that, in the case of size-independent growth (PBE is a convection equation), the diffusive term should be added, and the coefficient of the diffusive term is recommended as 2G × 10−3 to G × 10−2, where G is the crystal growth rate.

Sign in / Sign up

Export Citation Format

Share Document