A numerical approach for solving the high-order nonlinear singular Emden–Fowler type equations

Abstract

Reproducing kernel Hilbert space method (RKHSM) is an analytical technique, which can overcome the difficulty at the singular point of non-homogeneous, linear singular initial value problems; especially when the singularity appears on the right-hand side of this type of equations, so it can solve powerfully linear singular initial value problems. Therefore, using advantages of this method, in this paper the high-order nonlinear singular Emden-Fowler type equations are investigated by RKHSM. Then we present five numerical examples to show that the proposed scheme is accurate and reliable.

An efficient collocation algorithm for third order non-linear Emden–Fowler equation with multi-singularity

“…Wu and Li [21], present the analytical solution by applying the reproducing kernel algorithm of a class of third-order BVP. Further, In [22], the authors proposed the method for solving nonlinear singular Emden-Fowler type equations by applying the reproducing kernel Hilbert space algorithm. Aruna and Kanth [3] solve the third-order nonlinear singular BVPs by applying a numerical technique based on the differential transform algorithm.…”