Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 317, Issue -, Pages 307-330Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2016.11.026
Keywords
FPDEs; Riemann-Liouville fractional derivative; Collocation method; Legendre wavelet; Chebyshev wavelet; Operational matrix of differentiation and integration
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Funding
- Ministry of Human Resource and Development (MHRD), New Delhi, India under Senior Research Fellow (SRF) scheme
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In this article, we deal with a numerical wavelet collocation method (NWCM) using a technique based on two-dimensional wavelets (TDWs) approximation proposed for the fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media (EWDM). By implementing the Riemann-Liouville fractional derivative, TDWs approximation and its operational matrix along with collocation method are utilized to reduce FPDEs firstly into weakly singular fractional partial integro-differential equations (FPIDEs) and then reduced weakly singular FPIDEs into system of algebraic equation. Using Legendre wavelet approximation (LWA) and Chebyshev wavelet approximation (CWA), we investigated the convergence analysis and error analysis of the proposed problem. Finally, some examples are included for demonstrating the efficiency of the proposed method via LWA and CWA respectively. (C) 2016 Elsevier B.V. All rights reserved.
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