A novel numerical approach for the third order Emden-Fowler type equations

This article aims to achieve robust numerical results by applying the Chebyshev reproducing kernel method without homogenizing the initial-boundary conditions of the Emden-Fowler (E-F) equation, thereby introducing a new perspective to the literature. A novel numerical approach is presented for solving the initial-boundary value problem of third-order E-F equations using Chebyshev reproducing kernel theory. Unlike previous applications, which were confined to homogeneous initial-boundary value problems or required homogenization, the proposed method is effective for both homogeneous and nonhomogeneous cases. To handle the initial-boundary conditions of the E-F equations, additional basis functions are introduced rather than imposing conditions on the reproducing kernel Hilbert space. The method's effectiveness is demonstrated through five examples, which validate the theoretical analysis. Overall, the results emphasize the method's efficiency.