Treanor method

In a paper reporting the results of some simulations of diffusion of hydrogen into palladium [582], the authors describe their method of solution as the Treanor method. This is described in a few texts [314,351] and goes back to a paper by Treanor in 1966 [548]. 

The method is one way to handle a stiff set of odes, and is an extension of fourth-order explicit Runge-Kutta. The function to be solved is approximated over the next time interval by a combination of a linear function of the dependent variable and a quadratic function of time (assuming that it is strongly time-dependent) and this increases the accuracy and stability of the fourth-order Runge-Kutta method considerably. Today, however, we have other methods of dealing with stiff sets of odes, so this method might be said to have outlived its usefulness. 

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Reynolds CW (1987) Flocks, herds and schools a distributed behavioral model. Computer Graphics, ACM SIGGRAPH 87 Conference Proceedings Treanor G, Hinds BK (2000) Analysis of stresses in micro-drills using the finite element method. Int J Mach Tools Manufact 40(10) 1443-1456... 

Treanor CE (1966) A method for the numerical integration of coupled first-order diffeiential equations with greatly different time constants. Math Comput 20 39-45... 

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