2015
DOI: 10.1002/mma.3604
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Spectral meshless radial point interpolation (SMRPI) method to two‐dimensional fractional telegraph equation

Abstract: H. Ammari In this article, an innovative technique so‐called spectral meshless radial point interpolation (SMRPI) method is proposed and, as a test problem, is applied to a classical type of two‐dimensional time‐fractional telegraph equation defined by Caputo sense for (1 < α≤2). This new methods is based on meshless methods and benefits from spectral collocation ideas, but it does not belong to traditional meshless collocation methods. The point interpolation method with the help of radial basis functions is … Show more

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Cited by 53 publications
(17 citation statements)
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“…in where it has been used f (u (n) ) − f (U (n) ) L 2 ( ) ≤ M. By induction on Eq. (47) and that ξ (0) = 0, first when n = 0, we have ξ (1) L 2 ( ) ≤ C u δt 2 + a 0 γ sign(γ )M. Here C u , as mentioned before, is constant dependent only to the function u. Because b 0 = 1, then we can rewrite…”
Section: A the Stability And Convergence Analysismentioning
confidence: 84%
See 1 more Smart Citation
“…in where it has been used f (u (n) ) − f (U (n) ) L 2 ( ) ≤ M. By induction on Eq. (47) and that ξ (0) = 0, first when n = 0, we have ξ (1) L 2 ( ) ≤ C u δt 2 + a 0 γ sign(γ )M. Here C u , as mentioned before, is constant dependent only to the function u. Because b 0 = 1, then we can rewrite…”
Section: A the Stability And Convergence Analysismentioning
confidence: 84%
“…Shivanian [45][46][47][48] developed a kind of spectral meshless radial point interpolation (SMRPI) method, which is based on meshless methods and benefits from spectral collocation ideas, to present approximate solutions for some PDEs. In SMRPI technique, the point interpolation method with the help of those RBFs, which were free of shape parameter, has been proposed to construct shape functions which have Kronecker delta function property.…”
Section: Introductionmentioning
confidence: 99%
“…This section has been adopted from Ref. . Consider a continuous function u ( x ) defined in a domain Ω , which is represented by a set of field nodes.…”
Section: The Basis Functions In the Frame Of Mlrpimentioning
confidence: 99%
“…for more details about RPIM shape functions and the way they are constructed, the readers are referred to see [42].…”
Section: The Time Discretization Approximationmentioning
confidence: 99%
“…In the current work, we testify spectral meshless radial point interpolation (SMRPI) method [42][43][44] on the problem (1) and then make simulations on two numerical experiments which leads to satisfactory results. A technique based on radial point interpolation is adopted to construct shape functions, also called basis functions, using radial basis functions.…”
Section: Introductionmentioning
confidence: 99%