Verified integration of linear nth order ODEs using large steps
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摘要
The solution y(x) of an IVP for a linear ODE with analytic coefficient functions is represented as a power series. A high-order Taylor polynomial is used for an approximate numerical solution. The Taylor remainder series is rigorously estimated by some geometric series.The method has been implemented and tested on a computer. Guaranteed enclosures are achieved by taking into account all roundoff errors.
论文关键词：Ordinary differential equations,Initial value problems,Error bounds,Interval computations
论文评审过程：Available online 27 September 2006.
论文官网地址：https://doi.org/10.1016/j.amc.2006.08.033
