SOLVING MARKOVIAN SYSTEMS OF ODE FOR AVAILABILITY AND RELIABILITY CALCULATIONS

The computation of availability or reliability in a Markovian approach involves the solution of O.D.E.: dp/dt = L(t)p, where the transition matrix is time dependent, at least when some aggregation of the states is introduced to reduce the size of the problem. Methods of solution like uniformization are in this case unapplicable and we investigate h ere four explicit and six implicit R.K. methods from the point of view of stability, amount of numerical work and accuracy. The test problem chosen allows an analytical solution, a uniformization method (when L (t) is constant) and a fortiori all R.K. methods. The implicit trapezo idal rule used with a variable step scheme appears to be the best comp romise between accuracy and computational work.