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

Abstract The study presents a novel algorithm for solving third order non-linear equations (Emden-Fowler type) with multi-singularity, which can be applied to various physical models. The algorithm uses a quintic trigonometric B-spline collocation method and a quasilinearization technique to avoid the non-linearity term in the equation. The study establishes a comprehensive error analysis for the proposed algorithm and proves that it has O(h4) convergence. The algorithm’s ability to handle singular behavior at the point ς = 0 and its faster rate of convergence exhibits a promising approach to solve such problems. The study also validates the theoretical results through numerical experiments and shows that the proposed algorithm has a faster rate of convergence in comparison to the new cubic B-spline collocation method [1] and uniform Haar wavelet resolution technique [2]. Moreover, the new method has an edge (in terms of accuracy) over other existing methods, when applied to the problems [3–6]. 2000 Mathematics Subject Classification: 65L80; 65M99; 65N35; 34B16; 65L05; 65L10; 65N55.