Polynomial General Solutions for First Order Autonomous ODEs
نویسندگان
چکیده
For a first order autonomous ODE, we give a polynomial time algorithm to decide whether it has a polynomial general solution and to compute one if it exists. Experiments show that this algorithm is quite effective in solving ODEs with high degrees and a large number of terms.
منابع مشابه
A Polynomial Time Algorithm to Find Rational General Solutions of First Order Autonomous ODEs
We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order autonomous ODE F = 0, we give an exact degree bound for its rational solutions, based on the connection between rational solutions of F = 0 and rational parameterizations of the plane algebraic curve defined by F = 0. For a first order autonomous ODE, we further give a p...
متن کاملRational general solutions of first order non-autonomous parametrizable ODEs
In this paper we study non-autonomous algebraic ODEs F(x, y, y) = 0, where F(x, y, z) ∈ Q[x, y, z], provided a proper rational parametrization P (s, t) of the corresponding algebraic surface F(x, y, z) = 0. We show the relation between a rational general solution of the non-autonomous differential equation F(x, y, y) = 0 and a rational general solution of its associated autonomous system with r...
متن کاملA polynomial time algorithm for finding rational general solutions of first order autonomous ODEs
We improve the algorithm given in [3]. Through analysing the structural properties of a first order autonomous ODE with a rational solution, we give a polynomial time algorithm to find a rational general solution if it exists.
متن کاملA criterion for existence of rational general solutions of planar systems of ODEs
In the paper [Ngo09] we have studied the algebraic ODE of first order F (x, y, y′) = 0, where F ∈ Q[x, y, z], given its proper rational parametrization of the corresponding surface F (x, y, z) = 0. Using this proper parametrization we deduced the problem of finding rational general solutions of the equation F (x, y, y′) = 0 to finding rational general solutions of its associated system of ODEs ...
متن کاملRational solutions of ordinary difference equations
In this paper, we generalize the results of Feng and Gao [Feng, R., Gao, X.S., 2006. A polynomial time algorithm to find rational general solutions of first order autonomous ODEs. J. Symbolic Comput., 41(7), 735–762] to the case of difference equations. We construct two classes of ordinary difference equations (O∆Es) whose solutions are exactly the univariate polynomial and rational functions r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004