A multiscale collocation method for fractional differential problems

L. Pezza and F. Pitolli

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 147, issue C, 210-219

Abstract: We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown.

Keywords: Fractional differential problem; Collocation method; Fractional derivative; Fractional refinable function (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:147:y:2018:i:c:p:210-219

DOI: 10.1016/j.matcom.2017.07.005

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