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Approximate Solution of Fractional Differential Equations

Author: HuangLi
Tutor: LiXianFang
School: Hunan Normal University
Course: Applied Mathematics
Keywords: Taylor expansion Fractional Differential Equations Abel integral equation Initial value problem Approximate solution Error Analysis
CLC: O241.8
Type: Master's thesis
Year: 2007
Downloads: 452
Quote: 1
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Abstract


In this thesis five chapters , introduces the definition of fractional differential equations , properties and applications , the paper also provides an approximate solution that is fast and effective Taylor expansion method, by which gives the approximate solution of fractional differential equations . The first chapter describes the historical development of fractional differential equations , research status , as well as current international research on the issues related to basic mathematics . The second chapter focuses on the application of the Taylor expansion method for solving a simple form of fractional differential equations by numerical examples, illustrate the effectiveness of this method is simple . In the third chapter , based on the second chapter of this method is extended to more complex fractional differential equations , also by numerical examples show that the method of high accuracy and validity. In the fourth chapter discusses how to use the Taylor expansion method gives a similar type of fractional differential equations of two approximate solution of Abel integral equation and gives way to fix this , also through numerical examples show that the method is simple and effective and stability , show the advantages of this correction method . Chapter V summarizes the methods discussed earlier pointed out that the method is simple , effective, high-precision , and other basic features expected in theory can be further improved , and the use of more prospects .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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