论文标题
$ \ star $ - 产品求解器，具有光谱精度，用于非自治的普通微分方程
A $\star$-product solver with spectral accuracy for non-autonomous ordinary differential equations
论文作者
论文摘要
提出了一种解决非自治的普通微分方程的新方法，该方法可实现光谱精度。它基于一个新的结果，该结果表达了所谓的$ \ star $ -Algebra中的元素的解决方案。该代数配备了产品，即$ \ star $ - 产品，这是两个双变量分布的通常产品的组成部分。在Legendre多项式基础上扩展双变量分布会导致$ \ star $ - 产品的离散化，这允许通过求解线性方程式获得的向量近似解决方案。通过数值实验说明了这种方法的有效性。
A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called $\star$-algebra. This algebra is equipped with a product, the $\star$-product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions in bases of Legendre polynomials leads to a discretization of the $\star$-product and this allows for the solution to be approximated by a vector that is obtained by solving a linear system of equations. The effectiveness of this approach is illustrated with numerical experiments.
