A reliable numerical method for solving a certain class of singular initial value problems using reproducing kernel algorithm
For researchers working on singular differential equations, this offers a reliable numerical method, though it is an incremental application of existing RKHS techniques.
The paper presents a reproducing kernel Hilbert space method for solving Lane-Emden type singular initial value problems, demonstrating excellent agreement between numerical results and the analytical solution across several examples.
The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and introducing the reproducing kernel properties in which the initial conditions of the problem are satisfied. The analytical solution that obtained involves in the form of a convergent series with easily computable terms in its reproducing kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions and it is converge to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some examples to illustrate the accuracy, efficiency, and applicability of the method. The present work shows the potential of the RKHS technique in solving such nonlinear singular initial value problems.