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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical analysis, the Runge Kutta methods are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were developed around 1900 by the German mathematicians C. Runge and M.W. Kutta. See the article on numerical ordinary differential equations for more background and other methods. See also List of Runge Kutta methods. One member of the family of Runge Kutta methods is so commonly used that it is often referred to as "RK4", "classical Runge-Kutta method" or simply as "the Runge Kutta method".