The midpoint method is not the only second-order Runge Kutta method with two stages; there is a family of such methods, parameterized by ? and given by the formula
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Other adaptive Runge Kutta methods are the Bogacki Shampine method ( orders 3 and 2 ), the Cash Karp method and the Dormand Prince method ( both with orders 5 and 4 ).
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The weapon locating algorithm is an adaptive algorithm based on a modified version of the Runge-Kutta method, and uses Constant false alarm rate ( CFAR ) techniques to detect the target accurately.
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:The article Runge Kutta method ( SDE ) has a Markov chain approximation method that looks suitable to your problem .-- talk ) 18 : 05, 20 September 2013 ( UTC)
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I understand how to use Runge-Kutta methods to solve a first order differential equation, but I'm not sure how to adapt it to a second order equation like the harmonic oscillator.
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The two ordinary differential equations are solved using Runge-Kutta methods of orders 1, 3, and 5 with the same time step, to show the effects of computational accuracy in the results.
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Butcher showed that the Runge-Kutta method gives an " n " th order approximation of the actual flow provided that ? and ? agree on all trees with " n " nodes or less.
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This is especially useful when computing orbital dynamics, as many other integration schemes, such as the ( order-4 ) Runge-Kutta method, do not conserve energy and allow the system to drift substantially over time.
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The software produces finite difference equations that describe the graphical model and allows users to select a numerical analysis method to apply to the system, either the Euler method or various Runge Kutta methods ( either second or fourth order ).
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This makes the Euler method less accurate ( for small h ) than other higher-order techniques such as Runge-Kutta methods and linear multistep methods, for which the local truncation error is proportional to a higher power of the step size.
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