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|標題:||A wavelet operational method for solving fractional partial differential equations numerically||作者:||Wu, J.L.
|關鍵字:||Operational matrix;Fractional partial differential equations;Haar;wavelets;Numerical method;Lyapunov equation;series approach;system-identification;taylor-series;matrices||Project:||Applied Mathematics and Computation||期刊/報告no：:||Applied Mathematics and Computation, Volume 214, Issue 1, Page(s) 31-40.||摘要:||
Fractional calculus is an extension of derivatives and integrals to non-integer orders, and a partial differential equation involving the fractional calculus operators is called the fractional PDE. They have many applications in science and engineering. However not only the analytical solution existed for a limited number of cases, but also the numerical methods are very complicated and difficult. In this paper, we newly establish the simulation method based on the operational matrices of the orthogonal functions. We formulate the operational matrix of integration in a unified framework. By using the operational matrix of integration, we propose a new numerical method for linear fractional partial differential equation solving. In the method, we (1) use the Haar wavelet; (2) establish a Lyapunov-type matrix equation; and (3) obtain the algebraic equations suitable for computer programming. Two examples are given to demonstrate the simplicity, clarity and powerfulness of the new method. (C) 2009 Elsevier Inc. All rights reserved.
|Appears in Collections:||資訊網路與多媒體研究所|
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