Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods

Abstract

The struggle to find the analytic solution of several differential equations leads to several issues like difficulty in finding solutions, singularities, convergent issues, and stability. Because of these problems, most of the researchers come up with explicit approaches such as the Runge Kutta method, Euler’s method, and Taylor’s polynomial method for finding numerical solutions to the ordinary differential equation. In this work, we combine both the Aitken methods and Newton’s interpolation method (NIM) to solve first-order differential equations. The numerical results obtained provide minimal error. The result is supported by solving an example.

Keywords

• ordinary differential equation
• aitken’s method
• newton interpolation polynomial
• numerical approximation