High Quality Content by WIKIPEDIA articles! In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm of numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German mathematician Erwin Fehlberg and is based on the class of Runge–Kutta methods. The Runge–Kutta–Fehlberg method uses an O(h4) method together with an O(h5) method that uses all of the points of the O(h4) method, and hence is often referred to as an RKF45 method. Similar schemes with different orders have since been developed. By performing one extra calculation that would be required for an RK5 method, the error in the solution can be estimated and controlled and an appropriate step size can be determined automatically, making this method efficient for ordinary problems of automated numerical integration of ordinary differential equations.

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