A novel three-level time-split MacCormack scheme for two-dimensional evolutionary linear convection-diffusion-reaction equation with source term

2020 ◽  
pp. 1-28 ◽  
Author(s):  
Eric Ngondiep
Keyword(s):  
Source Term ◽  
Diffusion Reaction ◽  
Two Dimensional ◽  
Reaction Equation ◽  
Convection Diffusion ◽  
Maccormack Scheme

scholarly journals Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method

2013 ◽  
Vol 9 (17) ◽  
pp. 21-51 ◽  
Author(s):  
Carlos Bustamante ◽  
Henry Power ◽  
Whady Florez ◽  
Alan Hill Betancourt
Keyword(s):  
Numerical Scheme ◽  
Diffusion Reaction ◽  
Interpolation Function ◽  
Two Dimensional ◽  
Reaction Equation ◽  
Convection Diffusion ◽  
Non Linear ◽  
Newton Raphson ◽  
Hermitian Interpolation ◽  
Raphson Method

A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional do-mains. The Local Hermitian Interpolation (LHI) method is employed for thespatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same resultsare obtained for all the non-linear solvers tested, but better convergence ratesare attained with the Newton Raphson method in a double iteration scheme.

scholarly journals Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1878
Author(s):  
Eyaya Fekadie Anley ◽  
Zhoushun Zheng
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Diffusion Problem ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Finite Domain ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Nicolson Scheme ◽  
Crank Nicolson

In this paper, we have considered a numerical difference approximation for solving two-dimensional Riesz space fractional convection-diffusion problem with source term over a finite domain. The convection and diffusion equation can depend on both spatial and temporal variables. Crank-Nicolson scheme for time combined with weighted and shifted Grünwald-Letnikov difference operator for space are implemented to get second order convergence both in space and time. Unconditional stability and convergence order analysis of the scheme are explained theoretically and experimentally. The numerical tests are indicated that the Crank-Nicolson scheme with weighted shifted Grünwald-Letnikov approximations are effective numerical methods for two dimensional two-sided space fractional convection-diffusion equation.

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