<p>Herein, a composite numerical algorithm is developed with the sparse reconstruction of semi-orthogonal B-spline wavelets and Newton-Raphson method for the analysis and simulation of nonlinear singular Lane-Emden type models with different types of initial and boundary conditions. Lane-Emden models constitute a category of mathematical models which crop up in the field of astrophysics, theoretical physics, polytropic fluids etc. These models paraphrase the characteristics and composition of self-gravitating, compressible fluids in stars and gaseous spheres. In the design of the algorithm, compactly supported semi-orthogonal B-spline scaling and wavelet functions are used for spatial discretization and after that the obtained nonlinear system of equations is simulated by Newton-Raphson (NR) method. The convergence of the NR Method demonstrated by the theorem of spectral radius. Also, error analysis of B-spline wavelets is discussed and prove that the error bound is exponentially inversely proportional to the resolution level. In the end, the effectiveness of proposed method has been demonstrated through its application to the Bonner-Ebert gas sphere model, the second-kind Lane-Emden equation, the Emden-Fowler model, the Lane-Emden equation with polytropic index <i>p</i>, the heat conduction model in the human head, the White Dwarf equation and Lane-Emden type model.</p>