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A One-step Method of Order 10 for y″=f(x,y)

Published in IMA Journal of Numerical Analysis. 1982, vol. 2, no. 1, p. 83-94
Abstract In some situations, especially if one demands the solution of the differential equation with a great precision, it is preferable to use high-order methods. The methods considered here are similar to Runge-Kutta methods, but for the second-order equation y″=f(x,y). As for Runge-Kutta methods, the complexity of the order conditions grows rapidly with the order, so that we have to solve a non—linear system of 440 algebraic equations to obtain a tenth—order method. We demonstrate how this system can be solved. Finally we give the coefficients (20 decimals) of two methods with small local truncation errors.
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HAIRER, Ernst. A One-step Method of Order 10 for y″=f(x,y). In: IMA Journal of Numerical Analysis, 1982, vol. 2, n° 1, p. 83-94. doi: 10.1093/imanum/2.1.83

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Deposited on : 2010-11-15

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