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.

翻译：非自主线性普通差分方程式的解决方案在各种应用中都至关重要,例如核磁共振光谱分析。最近,在电弧中采用了一种具有光谱精度的新方法。该方法基于一种能够概括变化的产品。在这项工作中,我们表明有可能扩大该方法的用途,以解决非自主线性普通差分方程式(ODEs)的系统。在这种新方法中,ODE解决方案可以通过一个可以等同重写为矩阵方程式的线性系统来表达。数字示例说明了该方法的有效性和矩阵方程式解决方案的低等级属性。