Design and simulation of thin film anti-reflection coating on si-based photonic devices
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Publication Details
Author list: Prajakkan D., Bhatranand A., Jiraraksopakun Y.
Publisher: MDPI
Publication year: 2019
Journal: Mathematics (2227-7390)
Volume number: 7
Issue number: 10
Start page: 234
End page: 237
Number of pages: 4
ISSN: 2227-7390
eISSN: 2227-7390
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L2 and L∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before. © 2019 by the authors.
Keywords
Finite differences, Two-dimensional wavelets
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