A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations
نویسندگان
چکیده
منابع مشابه
A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations
A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations a,b Abstract Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure [16, 12, 13]. Apart from practical computational considerations, the method will be capable of telling us (u...
متن کاملv 1 1 4 Ju n 20 05 A semi - algorithm to find elementary first order invariants of rational second order ordinary differential equations
A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations a,b Abstract Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure [16, 12, 13]. Apart from practical computational considerations, the method will be capable of telling us (u...
متن کاملJu l 2 00 5 Finding Elementary First Integrals for Rational Second Order Ordinary Differential Equations
Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In [17], we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the present work. In [18], the authors used these results and developed a method to deal with SOODEs and a classification of those. Our present algorithm is based on ...
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2. General Remarks Second order ODEs are much harder to solve than first order ODEs. First of all, a second order linear ODE has two linearly independent solutions and a general solution is a linear combination of these two solutions. In addition, many popular second order ODEs have singular points. Except for a few cases, the solutions have no simple mathematical expression. However, there is ...
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We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz,w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation F (w′, w, z) = 0, (w′ = dw/dz) (1) where F is a polynomial in three variables. Theorem 1 For ...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2007
ISSN: 0096-3003
DOI: 10.1016/j.amc.2005.06.017