Details
| Original language | English |
|---|---|
| Article number | 173 |
| Journal | Advances in Difference Equations |
| Volume | 2021 |
| Issue number | 1 |
| Publication status | Published - 19 Mar 2021 |
Abstract
Linear differential equations usually arise from mathematical modeling of physical experiments and real-world problems. In most applications these equations are linked to initial or boundary conditions. But sometimes the solution under consideration is characterized by its asymptotic behavior, which leads to the question how to infer from the asymptotic growth of a solution to its initial values. In this paper we show that under some mild conditions the initial values of the desired solution can be computed by means of a continuous-time analogue of a modified matrix continued fraction. For numerical applications we develop forward and backward algorithms which behave well in most situations. The topic is closely related to the theory of special functions and its extension to higher-dimensional problems. Our investigations result in a powerful tool for solving some classical mathematical problems. To demonstrate the efficiency of our method we apply it to Poincaré type and Kneser’s differential equation.
Keywords
- Asymptotic behavior of solutions of linear differential equations, Kneser’s differential equation, Linear systems of difference and differential equations, Modified matrix-driven Jacobi–Perron algorithm, Poincaré–Perron-type differential equation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Algebra and Number Theory
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In: Advances in Difference Equations, Vol. 2021, No. 1, 173 , 19.03.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Computation of solutions to linear difference and differential equations with a prescribed asymptotic behaviour
AU - Baumann, Hendrik
AU - Hanschke, Thomas
PY - 2021/3/19
Y1 - 2021/3/19
N2 - Linear differential equations usually arise from mathematical modeling of physical experiments and real-world problems. In most applications these equations are linked to initial or boundary conditions. But sometimes the solution under consideration is characterized by its asymptotic behavior, which leads to the question how to infer from the asymptotic growth of a solution to its initial values. In this paper we show that under some mild conditions the initial values of the desired solution can be computed by means of a continuous-time analogue of a modified matrix continued fraction. For numerical applications we develop forward and backward algorithms which behave well in most situations. The topic is closely related to the theory of special functions and its extension to higher-dimensional problems. Our investigations result in a powerful tool for solving some classical mathematical problems. To demonstrate the efficiency of our method we apply it to Poincaré type and Kneser’s differential equation.
AB - Linear differential equations usually arise from mathematical modeling of physical experiments and real-world problems. In most applications these equations are linked to initial or boundary conditions. But sometimes the solution under consideration is characterized by its asymptotic behavior, which leads to the question how to infer from the asymptotic growth of a solution to its initial values. In this paper we show that under some mild conditions the initial values of the desired solution can be computed by means of a continuous-time analogue of a modified matrix continued fraction. For numerical applications we develop forward and backward algorithms which behave well in most situations. The topic is closely related to the theory of special functions and its extension to higher-dimensional problems. Our investigations result in a powerful tool for solving some classical mathematical problems. To demonstrate the efficiency of our method we apply it to Poincaré type and Kneser’s differential equation.
KW - Asymptotic behavior of solutions of linear differential equations
KW - Kneser’s differential equation
KW - Linear systems of difference and differential equations
KW - Modified matrix-driven Jacobi–Perron algorithm
KW - Poincaré–Perron-type differential equation
UR - http://www.scopus.com/inward/record.url?scp=85103356795&partnerID=8YFLogxK
U2 - 10.1186/s13662-021-03333-9
DO - 10.1186/s13662-021-03333-9
M3 - Article
VL - 2021
JO - Advances in Difference Equations
JF - Advances in Difference Equations
SN - 1687-1839
IS - 1
M1 - 173
ER -