非自治线性系常微分方程解的一种新的矩阵方程表示
A new matrix equation expression for the solution of non-autonomous linear systems of ODEs
摘要：
非自治线性常微分方程系统的解在许多应用中是至关重要的，例如核磁共振光谱学。最近在标量情况下引入了一种具有谱精度的新方法。该方法是基于一个产品，推广卷积。在这项工作中，我们表明，它是可能的方法来解决系统的非自治线性常微分方程（常微分方程）。在这种新方法中，常微分方程的解可以通过一个线性系来表示，该线性系可以等价地重写为矩阵方程。数值例子说明了该方法的有效性和矩阵方程解的低秩性质。
英文摘要：
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in the scalar case. The method is based on a product that generalizes the convolution. In this work, we show that it is possible to extend the method to solve systems of non-autonomous linear ordinary differential equations (ODEs). In this new approach, the ODE solution can be expressed through a linear system that can be equivalently rewritten as a matrix equation. Numerical examples illustrate the method's efficacy and the low-rank property of the matrix equation solution.
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