On the remainders of the asymptotic expansion of solutions of differential equations near irregular singular points
- 1 December 1994
- journal article
- research article
- Published by Taylor & Francis in Complex Variables and Elliptic Equations
- Vol. 26 (3) , 203-212
- https://doi.org/10.1080/17476939408814780
Abstract
We consider systems of linear differential equations with an irregular singular point of Poincaré rank 1 at infinity. It is well known that there is a fundamental system of formal solution vectors and, for each halfplane, a fundamental system of actual solution vectors having the formal ones as asymptotic expansions. These asymptotic expansions (in the sense of Poincaré) describe the behavior of the actual solutions as theindependent variable zgrows indefinitely, but give no precise error bounds for a given z, if the asymptotic series are truncated after Nterms. In this paper we show that for large values of |z| the best choice of Nis proportional to |z| and that the resulting error terms are exponentially small.Keywords
This publication has 6 references indexed in Scilit:
- Smoothing of the Stokes phenomenon for high-order differential equationsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Uniform asymptotic smoothing of Stokes’s discontinuitiesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1989
- Über das globale Verhalten der Normallösungen von x′(t) = (B + t−1A) x(t) und zweier Arten von assoziierten FunktionenMathematische Nachrichten, 1985
- On the Reduction of Connection Problems for Differential Equations with an Irregular Singular Point to Ones with Only Regular Singularities, ISIAM Journal on Mathematical Analysis, 1981
- Laplace integrals in singular differential and difference equationsPublished by Springer Nature ,1980
- Singular points of ordinary linear differential equationsTransactions of the American Mathematical Society, 1909