Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations

• Published in: Mathematical modelling and analysis Vol. 20; no. 6; pp. 754 - 767
• Main Authors: Azarnavid, Babak, Parvaneh, Foroud, Abbasbandy, Saeid
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.11.2015; Vilnius Gediminas Technical University
• Subjects: convergence; error estimate; Hilbert space; Iteration (Mathematics); Kernel functions; Mathematical research; Nonlinear differential equations; Picard iteration; reproducing kernel Hilbert space; singular nonlinear Lane-Emden type equations; error estimate; singular nonlinear Lane-Emden type equations; reproducing kernel Hilbert space; Picard iteration; convergence
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/13926292.2015.1111953

An iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove the convergence of the combined method. The numerical examples demonstrates a good agreement between numerical results and analytical predictions.