<p>This manuscript presents a new higher-order numerical discretization scheme for solving nonlinear third-order Emden-Fowler equations with local and nonlocal boundary conditions. Our approach is novel and highly efficient, as it can solve these problems without requiring the singularity and nonlinearity to be modified or eliminated, still maintaining high accuracy. In this approach, we discretize the solution domain into a uniform mesh and establish the higher-order compact scheme to approximate the first, second, third, and fourth derivatives that effectively deal with the singularity at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(t=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we discuss the theoretical convergence rate using a matrix analysis technique and also show that the rate of convergence of the proposed method aligns with its theoretical order. We solve several examples from existing literature and compare the numerical outcomes with other approaches to demonstrate the method’s efficiency and accuracy. The proposed scheme delivers better numerical solutions and achieves high-order exactness using a small-size matrix, making it more efficient than existing methods.</p>