Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations

• Published in: Computer Algebra in Scientific Computing Vol. 8136; pp. 140 - 147
• Main Authors: Grigoriev, Dima, Schwarz, Fritz
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2013; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: divisor of equations; multiple of equations; quasi-linear ordinary differential equations
• ISBN: 3319022962; 9783319022963
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-02297-0_12

If solutions of a non-linear differential equation may be obtained by specialization of solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say that the equation is a common multiple of the pair. We prove that a quasi-linear common multiple of a pair of quasi-linear equations always exists and design an algorithm which yields a quasi-linear common multiple.