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Series solutions to higher-order parametric boundary value problems

Jeffrey David J., Liang Songxin

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 2

31--40

Solving boundary value problems with parameters is challenging. Based on the homotopy analysis method, explicit formulas for the approximate solutions to a class of higher-order parametric boundary value problems are obtained. These explicit formulas give more insight into the solution structures of the given problems. The effectiveness of this approach is demonstrated by solving two specific parametric boundary value problems.

Further properties of the rational recursive sequence [formula]

Andruch-Sobiło A., Migda M.

Opuscula Mathematica

2006

Vol. 26, no. 3

387-394

In this paper we consider the difference equation [formula], n=0, 1... with positive parameters a and c, negative parameter b and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation (E).