Solving non-homogeneous lane-embed equation using Taylor series method

Abstract

This paper presents the approximate analytical solution for a lane-embedded non-homogeneous typeproblem using the Taylor series method. The Taylor series method stands as a fundamental mathematical tool for solving nonlinear differential equations, and in this work, its effectiveness is demonstrated by yielding highly accurate approximate solution with minimal iterations. Achieving higher derivatives in Taylor’s expansion is facilitated through the utilization of Maple software. Furthermore, in order to gain a comprehensive understanding of the system’s behavior, we conduct a comparison with the closed-form equation.