A uniform Haar wavelet collocation based method is proposed for finding the numerical results for a class of third order nonlinear (Emden–Fowler type) singular differential equations with initial and boundary conditions. At the point of singularity, the coefficient of the such equation blows up, that causes difficulties in capturing the numerical solutions near the point of singularity. Haar wavelet approach handles this peculiar situation efficiently. The proposed method is employed to reduce the IVPs/BVPs into the system of algebraic equations and the nonlinearity is taken care by Newton–Raphson method. It is demonstrated that, the method is appropriate for both initial as well as boundary conditions as these conditions are taken care automatically. Some numerical examples have been illustrated in order to demonstrate the ease of implementation and applicability of the method. The $L_2$ norm and absolute errors further help to manifest the improvement of the findings with the increase in resolution $J$. We compare our results with other methods which exists in literature, e.g., variation iteration method (VIM), cubic B-spline method, Differential transformation method (DTM), Iterative decomposition method (IDM) and modified Adomian decomposition method (MADM). The second order convergence and error analysis of the proposed method is established to depict the accuracy and stability of the proposed method.

提出了一种基于统一Haar小波配置的方法，用于寻找一类具有初始和边界条件的三阶非线性（Emden-Fowler型）奇异微分方程的数值结果。在奇点处，该等式的系数爆炸，这导致难以捕获奇点附近的数值解。Haar小波方法可有效处理这种特殊情况。提出的方法被用来将IVPs / BVPs简化为代数方程组，并且使用牛顿-拉夫森方法来解决非线性问题。结果表明，该方法既适用于初始条件也适用于边界条件，因为这些条件会自动处理。为了说明该方法的易于实施和适用性，已经说明了一些数值示例。的${\mathrm{大号}}_2$ 规范和绝对错误随着分辨率的提高进一步有助于证明研究结果的改进 $Ĵ$。我们将结果与文献中存在的其他方法进行比较，例如变异迭代方法（VIM），三次B样条方法，微分变换方法（DTM），迭代分解方法（IDM）和改进的Adomian分解方法（MADM）。建立了该方法的二阶收敛性和误差分析，以描述该方法的准确性和稳定性。