Euler method

The Euler method, also called the forward Euler method, is a first-order numerical procedure for solving ordinary differential equations when an initial value is given. It is the most basic explicit method of numerical integration for such equations and the simplest member of the Runge-Kutta family. It advances the solution in small steps, each time following the current slope of the solution over one step length. As a first-order method its error per step is proportional to the square of the step size, while the global error at a given time is proportional to the step size itself. It is named after Leonhard Euler, who proposed it in his book on integral calculus published between 1768 and 1770, and it often serves as the basis for building more complex methods such as predictor-corrector schemes.