A novel iterative solution for time-fractional Boussinesq equation by reproducing kernel method

• Published in: Journal of applied mathematics & computing Vol. 64; no. 1-2; pp. 227 - 254
• Main Authors: Sakar, Mehmet Giyas, Saldır, Onur
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020; Springer Nature B.V
• Subjects: Applied mathematics; Boussinesq equations; Computational Mathematics and Numerical Analysis; Hilbert space; Iterative methods; Iterative solution; Kernel functions; Linear operators; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operators (mathematics); Original Research; Theory of Computation; Reproducing kernel method; Fractional order; Boussinesq equation; 46E22; 35R11; 65M12; Convergence
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-020-01353-4

In this study, iterative reproducing kernel method (RKM) will be applied in order to observe the effect of the method on numerical solutions of fractional order Boussinesq equation. Hilbert spaces and their kernel functions, linear operators and base functions which are necessary to obtain the reproducing kernel function are clearly explained. Iterative solution is constituted in a serial form by using reproducing kernel function. Then convergence of RKM solution is shown with lemma and theorem. Two problems, “good” Boussinesq and generalized Boussinesq equations, are examined by using RKM for different fractional values. Results are presented with tables and graphics.