EULER POLYNOMIALS COLLOCATION METHOD FOR SOLVING LANE-EMDEN EQUATIONS - Kyato, Denen Dickson; Aboiyar, Terhemen (FUDMA JOURNAL OF SCIENCES, 2024)
In this paper, Euler polynomials were utilized to formulate a collocation method for approximating Lane-Emden equations. The approximation formulations were initialized producing truncation function. The residual functions were constructed by using the truncation function. The collocation points were substituted into the residual function to form system of equations and were solved by Matlab application fsolve or Newton-Raphson methods. The results were tabulated and compared with the Herodt (2004) results for absolute error. It was observed that the Euler polynomial is very accurate and converges faster producing zero error as compared. The study recommended in solving Lane-Emden and higher order equations.
Keywords: Lane-Emden Equations; Euler Polynomials; Collocation method; Truncation function; Residual function; System of equations