A fast and faithful collocation method with efficient matrix assembly for a two-dimensional nonlocal diffusion model

2014 ◽  
Vol 273 ◽  
pp. 19-36 ◽  
Author(s):  
Hong Wang ◽  
Hao Tian
Keyword(s):  
Collocation Method ◽  
Diffusion Model ◽  
Nonlocal Diffusion ◽  
Two Dimensional ◽  
Matrix Assembly

scholarly journals Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xuhao Zhang ◽  
Aijie Cheng
Keyword(s):  
Collocation Method ◽  
Diffusion Model ◽  
Variable Coefficient ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Coefficient Matrix ◽  
Nonlocal Diffusion ◽  
Two Dimensional ◽  
Subspace Iteration ◽  
Dimensional Variable

Abstract In this paper, a fast collocation method is developed for a two-dimensional variable-coefficient linear nonlocal diffusion model. By carefully dealing with the variable coefficient in the integral operator and then analyzing the structure of the coefficient matrix, we can reduce the computational operations in each Krylov subspace iteration from $O(N^{2})$ O ( N 2 ) to $O(N\log N)$ O ( N log N ) and the memory requirement for the coefficient matrix from $O(N^{2})$ O ( N 2 ) to $O(N)$ O ( N ) . Numerical experiments are carried out to show the utility of the fast collocation method.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

Moving and jumping spot in a two-dimensional reaction–diffusion model

Nonlinearity ◽  
2017 ◽  
Vol 30 (4) ◽  
pp. 1536-1563 ◽  
Author(s):  
Shuangquan Xie ◽  
Theodore Kolokolnikov
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Two Dimensional ◽  
Reaction Diffusion Model
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