梁振动方程数值解的移位Legendre小波配置法
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摘要
建立了求解梁振动方程数值解的移位Legendre小波配置法。利用移位的Legendre多项式,推导出Riemann-Liouville意义下移位Legendre小波函数的一般分数阶积分公式。利用分数积分公式和二维移位Legendre小波配置法,将梁振动方程求解问题转化为代数方程组求解。数值算例表明该方法具有较高的精度。
Collocation method based on Shifted Legendre wavelet for solving the numerical solution of beam vibration equation is presented. The fractional integral formula of a single shifted Legendre wavelet function is derived from the definition by means of the shifted Legendre polynomial. Beam vibration equation is converted to a system of algebraic equation by using two dimensional shifted Legendre wavelet collocation methods and fractional integral formula. Numerical example shows that the method has high accuracy.
Collocation method based on Shifted Legendre wavelet for solving the numerical solution of beam vibration equation is presented. The fractional integral formula of a single shifted Legendre wavelet function is derived from the definition by means of the shifted Legendre polynomial. Beam vibration equation is converted to a system of algebraic equation by using two dimensional shifted Legendre wavelet collocation methods and fractional integral formula. Numerical example shows that the method has high accuracy.
引文
李红星,赵烽帆,郑敏娜.2014.小波分析在天然地震初震及震相识别中的应用[J].东华理工大学学报(自然科学版),37(3):286-291.
李麦侠,曲小钢.2013.梁振动问题的MOL数值方法[J].陕西科技大学学报,31(6):166-168.
李鑫.2016.梁振动方程一类稳定的紧致差分格式[J].安徽科技学院学报,30(4):50-56.
单双荣.2006.梁振动方程的多辛Fourier拟谱算法[J].华侨大学学报(自然科学版),27(3):234-237.
石方圆,李书存.2018.梁振动方程的三点稳定紧致差分格式[J].河北师范大学学报(自然科学版),42(1):19-23.
宋志伟,李威,渠鸿飞.2012.拟小波方法在梁动力稳定性分析中的应用[J].土木工程与管理学报,29(2):113-118.
王兰.2015.杆振动方程的高阶紧致差分格式[J].江西师范大学学报(自然科学版),39(4):351-354.
曾文平.2004.四阶杆振动方程的两类高精度辛格式[J].高等学校计算数学学报,26(4):378-384.
朱莉.2017.分数阶偏微分方程的小波算子矩阵解法[J].厦门理工学院学报,25(3):75-82.
邹佩,曲小钢.2011.梁振动问题的拟小波精细时程积分法[J].陕西科技大学学报,29(6):140-143.
Barikbin Z.2017.Two-dimensional Bernoulli wavelets with satisfier function in the Ritz-Galerkin method for the time fractional diffusionwave equation with damping[J].Mathematical Sciences,11(3):195-202.
Gupta A K,Ray S S.2015.Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method[J].Applied Mathematical Modelling,39(17):121-130.
Liu N,Lin E.2010.Legendre wavelet method for numerical solutions of partial differential equations[J].Numerical Methods for Partial Differential Equations,26(1):81-94.
Podlubny I.1999.Fractional Differential Equations[M].Academic Press,San Diego.
李麦侠,曲小钢.2013.梁振动问题的MOL数值方法[J].陕西科技大学学报,31(6):166-168.
李鑫.2016.梁振动方程一类稳定的紧致差分格式[J].安徽科技学院学报,30(4):50-56.
单双荣.2006.梁振动方程的多辛Fourier拟谱算法[J].华侨大学学报(自然科学版),27(3):234-237.
石方圆,李书存.2018.梁振动方程的三点稳定紧致差分格式[J].河北师范大学学报(自然科学版),42(1):19-23.
宋志伟,李威,渠鸿飞.2012.拟小波方法在梁动力稳定性分析中的应用[J].土木工程与管理学报,29(2):113-118.
王兰.2015.杆振动方程的高阶紧致差分格式[J].江西师范大学学报(自然科学版),39(4):351-354.
曾文平.2004.四阶杆振动方程的两类高精度辛格式[J].高等学校计算数学学报,26(4):378-384.
朱莉.2017.分数阶偏微分方程的小波算子矩阵解法[J].厦门理工学院学报,25(3):75-82.
邹佩,曲小钢.2011.梁振动问题的拟小波精细时程积分法[J].陕西科技大学学报,29(6):140-143.
Barikbin Z.2017.Two-dimensional Bernoulli wavelets with satisfier function in the Ritz-Galerkin method for the time fractional diffusionwave equation with damping[J].Mathematical Sciences,11(3):195-202.
Gupta A K,Ray S S.2015.Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method[J].Applied Mathematical Modelling,39(17):121-130.
Liu N,Lin E.2010.Legendre wavelet method for numerical solutions of partial differential equations[J].Numerical Methods for Partial Differential Equations,26(1):81-94.
Podlubny I.1999.Fractional Differential Equations[M].Academic Press,San Diego.