Michelsen semi-implicit

The semi-implicit Michelsen method has the advantage of being third order and strongly A-stable without requiring, as per the implicit methods, the solution of a nonlinear system. Moreover, the control of the error can be performed with an embedded first-order method, also strongly A-stable. 

The following algorithm for semi-implicit third order Rimge-Kutta is suggested by Michelsen (1976) for the following equation... 

Michelsen s third order semi-implicit Runge-Kutta method is a modified version of the method originally proposed by Caillaud and Padmanabhan (1971). This third-order semi-implicit method is an improvement over the original version of semi-implicit methods proposed in 1963 by Rosenbrock. 

Perform the integration in Problem 73 using the semi-implicit formula of Michelsen (Eq. 7.126) with a constant step size. 

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