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Haghighi, Ahmad Reza
- The Fractional Cubic Spline Interpolation without Using the Derivative Values
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Authors
Affiliations
1 Department of Mathematics, Urmia University of Technology, Urmia, IR
1 Department of Mathematics, Urmia University of Technology, Urmia, IR
Source
Indian Journal of Science and Technology, Vol 5, No 10 (2012), Pagination: 3433-3439Abstract
The paper introduces a function value based fraction of cubic spline interpolation, which is used for studying the curves and surfaces. The interpolation function has a simple and explicit mathematical representation, convenient both in practical application and in theoretical studies. It should be mentioned that the interpolating surfaces are C1 in the interpolating region under the condition that the interpolation is only based on the function values. Moreover, properties and views are shown in matrix notation, and then the error is calculated.Keywords
Fractional Spline, Fractional Interpolation: Spline Interpolation Function, Peano Kernel TheoremFull Text
References
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- Explicit and Implicit Methods for Fractional Diffusion Equations with the Riesz Fractional Derivative
Abstract Views :500 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Urmia University of Technology, Urmia, IR
2 Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, IR
1 Department of Mathematics, Urmia University of Technology, Urmia, IR
2 Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, IR
Source
Indian Journal of Science and Technology, Vol 6, No 7 (2013), Pagination: 4881-4885Abstract
In this paper, a fractional diffusion equation by using the explicit numerical method in a finite domain with second-order accuracy which includes the Riesz fractional derivative approximation is studied. For the Riesz fractional derivative approximation, ''fractional centered derivative'' approach is used. The error of the Riesz fractional derivative to the fractional centered difference is calculated. We used the implicit numerical method to solve the fractional diffusion equation and also investigated the stability of explicit and implicit methods. The maximum error of the implicit method for fractional diffusion equation with using fractional centered difference approach is shown by using the numerical results.Keywords
Riesz Fractional Derivative Operator, Implicit Method, Explicit Method, Fractional Central DifferenceFull Text
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