<p>In this article, the numerical solution of the coupled third-order Emden-Fowler type equation is obtained subject to initial, two-point, and three-point (nonlocal) boundary conditions. The truncated Taylor wavelet series is employed to approximate the third-order derivative of the unknown functions. This wavelet series and its integrals express the given coupled model into a pair of equations with unknown coefficients to be determined. The collocation method is then applied to reduce them further into a system of algebraic equations, which can be straightforwardly solved using Newton’s method. Finally, numerical experiments are conducted to demonstrate that the proposed method is effective. The numerical outcomes are evaluated using maximum absolute error and residual error. This approach handles singularity directly and gives reliable solutions. Also, the localization property of the wavelet approach enables desirable accuracy for a few collocation points. Further, convergence and error bounds are discussed for the Taylor wavelets approximation.</p>