scholarly journals A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

2019 ◽  
Vol 42 (10) ◽  
pp. 3465-3480 ◽  
Author(s):  
Mohammed K. Almoaeet ◽  
Mostafa Shamsi ◽  
Hassan Khosravian‐Arab ◽  
Delfim F. M. Torres
Keyword(s):  
Collocation Method ◽  
Method Of Lines ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Advection Diffusion

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.

scholarly journals Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Joan Goh ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Test Problems ◽  
Spline Collocation ◽  
Von Neumann ◽  
One Dimensional ◽  
Advection Diffusion ◽  
The Stability ◽  
Good Agreement

Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubicB-spline. Usual finite difference scheme is used for time and space integrations. CubicB-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.

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