عادل راشد عبد علي
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A. R. A. Ali
PhD
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lecturer
College of Education for Pure Sciences (Ibn Al-Haitham)
,
Department of Mathematics
[email protected]
Publication Date
Wed Jul 01 2020
Journal Name
Journal Of Physics: Conference Series
A Multilevel Approach for Stability Conditions in Fractional Time Diffusion Problems
Abstract<p>The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr</p>
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Publication Date
Wed Jul 01 2020
Journal Name
Journal Of Physics: Conference Series
Improved Alternating Direction Implicit Method
Abstract<p>The alternating direction implicit method (ADI) is a common classical numerical method that was first introduced to solve the heat equation in two or more spatial dimensions and can also be used to solve parabolic and elliptic partial differential equations as well. In this paper, We introduce an improvement to the alternating direction implicit (ADI) method to get an equivalent scheme to Crank-Nicolson differences scheme in two dimensions with the main feature of ADI method. The new scheme can be solved by similar ADI algorithm with some modifications. A numerical example was provided to support the theoretical results in the research.</p>
(1)
Publication Date
Fri Jan 01 2016
Journal Name
Pure And Applied Mathematics Journal
(2)
Publication Date
Fri Jan 01 2016
Journal Name
Applied And Computational Mathematics
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