Two Dimensional Tensor Product B-spline Wavelet Scaling Functions for Solution of Two-Dimensional Steady Navier-Stokes (NS) Equations

2009 ◽  
Author(s):  
Xiong Lei ◽  
Liu KeZhong ◽  
Zhu ZhenHuan ◽  
Wen YuanQiao ◽  
Mu JunMin ◽  
...  
Keyword(s):  
Tensor Product ◽  
Navier Stokes ◽  
Scaling Functions ◽  
Two Dimensional ◽  
Spline Wavelet ◽  
B Spline

Multiscale Products in B-spline Wavelet Domain: A New Method for Short Exon Detection

2018 ◽  
Vol 13 (5) ◽  
pp. 553-563 ◽  
Author(s):  
Xiaolei Zhang ◽  
Guishan Zhang ◽  
Yangjiang Yu ◽  
Guocheng Pan ◽  
Haitao Deng ◽  
...  
Keyword(s):  
New Method ◽  
Wavelet Domain ◽  
Spline Wavelet ◽  
B Spline ◽  
Short Exon ◽  
Multiscale Products

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

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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