Synchronization of the nonlinear advection‐diffusion‐reaction processes

2020 ◽  
Author(s):  
Murat Sari ◽  
Shko Ali Tahir
Keyword(s):  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Nonlinear Advection ◽  
Reaction Processes

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.

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hamid Mesgarani ◽  
Mahya Kermani ◽  
Mostafa Abbaszadeh
Keyword(s):  
Method Of Lines ◽  
Variable Coefficients ◽  
Diffusion Reaction ◽  
Test Problems ◽  
Reaction Equation ◽  
Content Type ◽  
Interpolation Matrix ◽  
Advection Diffusion ◽  
The Method Of Lines ◽  
Nonlinear Advection

Purpose The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients. Design/methodology/approach The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well. Findings Several test problems are provided to confirm the validity and efficiently of the proposed method. Originality/value For the first time, some famous examples are solved by using the proposed high-order technique.

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