An Operator-Based Scheme for the Numerical Integration of FDEs

• Published in: Mathematics (Basel) Vol. 9; no. 12; p. 1372
• Main Authors: Timofejeva, Inga, Navickas, Zenonas, Telksnys, Tadas, Marcinkevicius, Romas, Ragulskis, Minvydas
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-06-2021
• Subjects: Algorithms; Approximation; Differential equations; Exact solutions; fractional differential equation; generalized differential operator; Mathematical analysis; Mathematics; Numerical integration; Operators (mathematics); Partial differential equations; Polynomials; Power series
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9121372

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.