RICHARDSON EXTRAPOLATION OF ITERATED DISCRETE COLLOCATION METHOD FOR EIGENVALUE PROBLEM OF A TWO DIMENSIONAL COMPACT INTEGRAL OPERATOR

2014 ◽  
Vol 32 (5_6) ◽  
pp. 567-584
Author(s):  
Bijaya Laxmi Panigrahi ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Integral Operator ◽  
Eigenvalue Problem ◽  
Collocation Method ◽  
Richardson Extrapolation ◽  
Two Dimensional ◽  
Compact Integral Operator

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.

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