کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645473 | 1342038 | 2012 | 20 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs](/preview/png/4645473.png)
We consider time-averaging methods based on the Magnus series expansion jointly with exponential integrators for the numerical integration of general linear non-homogeneous differential equations. The schemes can be considered as averaged methods which transform, for one time step, a non-autonomous problem into an autonomous one whose flows agree up to a given order of accuracy at the end of the time step. The problem is reformulated as a particular case of a matrix Riccati differential equation and the Möbius transformation is considered, leading to a homogeneous linear problem. The methods proposed can be used both for initial value problems (IVPs) as well as for two-point boundary value problems (BVPs). In addition, they allow to use different approximations for different parts of the equation, e.g. the homogeneous and non-homogeneous parts, or to use adaptive time steps. The particular case of separated boundary conditions using the imbedding formulation is also considered. This formulation allows us to transform a stiff and badly conditioned BVP into a set of well conditioned IVPs which can be integrated using some of the previous methods. The performance of the methods is illustrated on some numerical examples.
Journal: Applied Numerical Mathematics - Volume 62, Issue 8, August 2012, Pages 875-894