A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary differential equation which is subsequently solved with numerical integrators obtained from the Magnus expansion. The algorithm can be used in the periodic case to get both accurate approximations of the characteristic multipliers and the solution itself. In addition, it can be extended to deal with certain quasilinear delay equations.
翻译:介绍了一种在数字上整合非自动线性延缓分方程的程序,其基础是使用延迟部分的光谱分解法将原问题转换成矩阵线性普通差分方程,随后通过从Magnus扩展中获取的数字集成器来解决,在定期案例中,可以使用算法获得特征乘数和解决方案本身的准确近似值。此外,还可以扩大算法,以处理某些准线性延缓方程。