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The aim of this study is to give a Legendre polynomial approximation for the solution of the second order linear hyper-bolic partial differential equations (HPDEs) with two variables and constant coefficients. For this purpose, Legendre matrix method for the approximate solution of the considered HPDEs with specified associated conditions in terms of Legendre polynomials at any point is introduced. The method is based on taking truncated Legendre series of the functions in the equation and then substituting their matrix forms into the given equation. Thereby the basic equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Legendre coefficients. The result matrix equation can be solved and the unknown Legendre coefficients can be found approximately. Moreover, the approximated solutions of the proposed method are compared with the Taylor [1] and Bernoulli [2] matrix methods. All of computations are performed on a PC using several programs written in MATLAB 7.12.0.
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篇名 Legendre Approximation for Solving Linear HPDEs and Comparison with Taylor and Bernoulli Matrix Methods
来源期刊 应用数学(英文) 学科 数学
关键词 LEGENDRE OPERATIONAL Matrix of Differentiation HYPERBOLIC Partial Differential Equations LEGENDRE POLYNOMIAL Solutions Double LEGENDRE Series
年,卷(期) 2012,(5) 所属期刊栏目
研究方向 页码范围 410-416
页数 7页 分类号 O1
字数 语种
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节点文献
LEGENDRE
OPERATIONAL
Matrix
of
Differentiation
HYPERBOLIC
Partial
Differential
Equations
LEGENDRE
POLYNOMIAL
Solutions
Double
LEGENDRE
Series
研究起点
研究来源
研究分支
研究去脉
引文网络交叉学科
相关学者/机构
期刊影响力
应用数学(英文)
月刊
2152-7385
武汉市江夏区汤逊湖北路38号光谷总部空间
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1878
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0
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