DEVELOPMENT OF SOME BLOCK LINEAR MULTISTEP METHOD FOR THE NUMERICAL SOLUTION OF LANE–EMDEN TYPE EQUATIONS

This research paper presents the development of some Block Linear Multistep Methods (BLMM) for the numerical solution of Lane–Emden type equations, which are nonlinear second-order ordinary differential equations with singularities. The proposed methods employ collocation and interpolation techniques based on a power-series approximation. Two block schemes, corresponding to K=4 and K=5, were derived with uniform orders six and seven, respectively. In obtaining accuracy and efficiency, three classical Lane–Emden problems were solved using two different step sizes of, h=0.01 and h=0.005. Numerical results show that the method achieves high accuracy, with absolute errors consistently ranging from 10−10 to 10−12 . The comparison of the results for both step sizes shows that the proposed methods are accurate, stable, and effective for solving this class of singular problems.