Chebyshev多项式展开的数值逼近
Numerical Approximations Using Chebyshev Polynomial Expansions
摘要：
我们提出的数值解微分方程通过扩大未知函数的Chebyshev多项式和线性方程组直接求解的值的函数在极值（或零）的Chebyshev多项式阶N（埃尔-根迪的方法）。在这些点上的解决方案是准确的，除了四舍五入的计算机错误和收敛的其他数值方法用于解决线性方程组。应用于含时量子场论的初值问题和流体动力学的二阶边值问题。
英文摘要：
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.
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