Physics – Mathematical Physics
Scientific paper
2008-11-10
Ann. Phys. 323 (2008) 3074-3090
Physics
Mathematical Physics
Latex file, 27 pages, 2 figures, 5 tables
Scientific paper
10.1016/j.aop.2008.05.009
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward two-step procedure. First, the solution to an equation is represented as an asymptotic series in powers of a variable. Second, the series are summed by means of the self-similar factor approximants. The obtained expressions provide highly accurate approximate solutions to the considered equations. In some cases, it is even possible to reconstruct exact solutions for the whole region of variables, starting from asymptotic series for small variables. This can become possible even when the solution is a transcendental function. The method is shown to be more simple and accurate than different variants of perturbation theory with respect to small parameters, being applicable even when these parameters are large. The generality and accuracy of the method are illustrated by a number of evolution equations as well as boundary value problems.
Gluzman Simon
Yukalov V. I.
Yukalova E. P.
No associations
LandOfFree
Self-similar factor approximants for evolution equations and boundary-value problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Self-similar factor approximants for evolution equations and boundary-value problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-similar factor approximants for evolution equations and boundary-value problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-724676