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

Abstract

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.

Keywords:

• reproducing kernel Hilbert space
• Picard iteration
• error estimate
• convergence
• singular nonlinear Lane-Emden type equations

AMS Subject Classification:

• 65L05
• 46E22
• 34B16