Numerical solution of nonlinear advection diffusion reaction equation using high-order compact difference method

2021 ◽  
Author(s):  
Lin Zhang ◽  
Yongbin Ge
Keyword(s):  
Numerical Solution ◽  
Difference Method ◽  
High Order ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Compact Difference ◽  
Advection Diffusion ◽  
Nonlinear Advection ◽  
Compact Difference Method

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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