Approximation of solutions to nonautonomous difference equations

Year, pages: 2019, 109 - 121

We study the asymptotic properties of solutions to nonautonomous difference equations of the form \[ \D^m x_n=a_nf(n,x_{\sigma(n)})+b_n, \quad f\colon \N\times\R\to\R, \quad \sigma\colon \N\to\N. \] Using the iterated remainder operator and asymptotic difference pairs we establish some results concerning approximative solutions and approximations of~solutions. Our approach allows us to control the degree of approximation.

Migda, J., Migda, M. 2019. Approximation of solutions to nonautonomous difference equations. In Tatra Mountains Mathematical Publications, vol. 71, no.1, pp. 109-121. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0010

Migda, J., Migda, M. (2019). Approximation of solutions to nonautonomous difference equations. Tatra Mountains Mathematical Publications, 71(1), 109-121. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0010

Publisher: MÚ SAV