论文标题
线性和准线性延迟微分方程的Magnus积分器
Magnus integrators for linear and quasilinear delay differential equations
论文作者
论文摘要
提出了一种数值整合非自治线性延迟差分方程的程序。它基于使用延迟零件的光谱离散化将原始问题转换为矩阵线性普通微分方程，随后用从Magnus膨胀获得的数值积分器来求解。该算法可以在周期性的情况下使用，以获得特征乘数和解决方案本身的准确近似值。此外，可以将其扩展以处理某些准线性延迟方程。
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.
