General Lagrange scaling functions: application in general model of variable order fractional partial differential equations

2021 ◽  
Vol 40 (8) ◽  
Author(s):  
Sedigheh Sabermahani ◽  
Yadollah Ordokhani ◽  
Hossein Hassani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
General Model ◽  
Scaling Functions ◽  
Variable Order ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

B-spline wavelet operational method for numerical solution of time-space fractional partial differential equations

2017 ◽  
Vol 15 (04) ◽  
pp. 1750034 ◽  
Author(s):  
Zeynab Kargar ◽  
Habibollah Saeedi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Results ◽  
Scaling Functions ◽  
Operational Matrices ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
B Spline ◽  
Time Space ◽  
Linear B

In this paper, the linear B-spline scaling functions and wavelets operational matrix of fractional integration are derived. A new approach implementing the linear B-spline scaling functions and wavelets operational matrices combining with the spectral tau method is introduced for approximating the numerical solutions of time-space fractional partial differential equations with initial-boundary conditions. They are utilized to reduce the main problem to a system of algebraic equations. The uniform convergence analysis for the linear B-spline scaling functions and wavelets expansion and an efficient error estimation of the presented method are also introduced. Illustrative examples are given and numerical results are presented to demonstrate the efficiency and accuracy of the proposed method. Special attention is given to a comparison between the numerical results obtained by our new technique and those found by other known methods.

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