A fully discrete H 1-Galerkin method with quadrature for nonlinear advection–diffusion–reaction equations

2007 ◽  
Vol 43 (4) ◽  
pp. 355-383 ◽  
Author(s):  
M. Ganesh ◽  
K. Mustapha
Keyword(s):  
Galerkin Method ◽  
Diffusion Reaction ◽  
Fully Discrete ◽  
Advection Diffusion ◽  
Nonlinear Advection ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations

scholarly journals Numerical study of 1D and 2D advection-diffusion-reaction equations using Lucas and Fibonacci polynomials

2021 ◽  
Author(s):  
Ihteram Ali ◽  
Sirajul Haq ◽  
Kottakkaran Sooppy Nisar ◽  
Shams Ul Arifeen
Keyword(s):  
Numerical Study ◽  
Diffusion Reaction ◽  
Test Problems ◽  
Algebraic Equations ◽  
Fibonacci Polynomials ◽  
Advection Diffusion ◽  
Nonlinear Advection ◽  
The Given ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations

AbstractIn this work, a numerical scheme based on combined Lucas and Fibonacci polynomials is proposed for one- and two-dimensional nonlinear advection–diffusion–reaction equations. Initially, the given partial differential equation (PDE) reduces to discrete form using finite difference method and $$\theta -$$ θ - weighted scheme. Thereafter, the unknown functions have been approximated by Lucas polynomial while their derivatives by Fibonacci polynomials. With the help of these approximations, the nonlinear PDE transforms into a system of algebraic equations which can be solved easily. Convergence of the method has been investigated theoretically as well as numerically. Performance of the proposed method has been verified with the help of some test problems. Efficiency of the technique is examined in terms of root mean square (RMS), $$L_2$$ L 2 and $$L_\infty $$ L ∞ error norms. The obtained results are then compared with those available in the literature.

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