A Comparison of Interpolation and Least Squares Methods for the Approximate Solution of Differential Equation

The aim of this article is to assist novice students in understanding and applying numerical analysis techniques. This article presents a comparison between the numerical methods of least squares and Newton's interpolation for solving differential equations with boundary conditions. Two case studies are examined where these methodologies are applied, generating polynomial solutions of degree 20. Both methods demonstrate high accuracy, despite differences in the magnitude and signs of the coefficients for each power forming the polynomial. The solution obtained via interpolation exhibits better accuracy compared to LMS, with an improvement of up to 8 orders of magnitude near the right boundary.