Comparison between Euler and Taylor Method

Euler Method:

In mathematics and computational science, the Euler method is a first-order numerical procedure for solving ordinary differential equations with a given initial value. It is the most basic explicit method for the numerical integration of ordinary differential equations and is the simplest Runge–Kutta method.

Applications of Euler Method:

1. Konigsberg Bridge problem, Euler circuits and paths are also useful to painters, garbage collectors, airplane pilots, and all world navigators.
2. The Euler Method is used in solving ODEs, estimating the Force-Deformation behavior in the non-linear range, Euler applications in the stability of structures and earthquake engineering and structural dynamics.

Taylor Method:

In calculus, Taylor’s theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.

Application of Taylor Method:

1. The Galerkin Computational Fluid Dynamics, The cumulants (some expectation value or variance of statistical data), The current-mode pseudo-exponential circuit, the Dirichlet-Neumann operator (used in analyzing boundary conditions e.g fluid dynamics and crystal growth).
2. The Taylor Series is used in power flow analysis of electrical power systems, Generating functions.

Comparison between Euler and Taylor Method: