论文标题
基于转移的卢卡斯多项式的新小波方法：tau方法
New wavelet method based on Shifted Lucas polynomials: A tau approach
论文作者
论文摘要
在当前的工作中，引入了非熟悉的Lucas多项式。我们已经构建了一种计算小波技术，用于解决初始/边界值二阶微分方程的解决方案。对于此数值方案，我们为Lucas多项式开发了体重函数和Rodrigues的公式。此外，Lucas多项式及其特性用于提出移动的Lucas多项式，然后利用移动的Lucas多项式为我们提供了转移的Lucas小波。我们提供了分化的操作矩阵和转移的Lucas小波的产品运行矩阵。此外，收敛和误差分析确保了提出的方法的准确性。说明性示例表明，目前的方法在数值上是富有成果，有效且方便的，可用于求解微分方程
In current work, non-familiar shifted Lucas polynomials are introduced. We have constructed a computational wavelet technique for solution of initial/boundary value second order differential equations. For this numerical scheme, we have developed weight function and Rodrigues' formula for Lucas polynomials. Further, Lucas polynomials and their properties are used to propose shifted Lucas polynomials and then utilization of shifted Lucas polynomials provides us shifted Lucas wavelet. We furnished the operational matrix of differentiation and the product operational matrix of the shifted Lucas wavelets. Moreover, convergence and error analysis ensure accuracy of the proposed method. Illustrative examples show that the present method is numerically fruitful, effective and convenient for solving differential equations
