obtained by the sampling of actual (i.e., measured) forcing 

 function records. Thus, these simulation studies require: 



(1) Algorithms employing random number generators 

 and digital filtering techniques for the 

 generation of synthetic correlated input 

 sequences having characteristics which can 



be adjusted to closely match those of se- 

 quences which can be expected from the 

 sampling of actual wave data, and 



(2) Efficient and "statistically accurate" algo- 

 rithms for the numerical solution of the 

 non-linear state equations of the system for 

 random inputs as described. 



In regard to the second requirement , there are numerous 

 approaches to the problem of numerically integrating both linear 

 and non-linear differential state equations, and several compari- 

 sons of various methods have been made (e.g., Martens, 1969) for 

 homogeneous equations or equations with simple specified 

 (deterministic) forcing functions. A comparison of simulation 

 algorithms (based on mean-square error criterion) for systems 

 with random inputs has recently been completed (Kim, 1978). In 

 this study, the system models included simple first and second 

 order linear systems, and two highly simplified non-linear models 

 for an ocean platform and a moored ship, respectively. The input 

 signals used consisted of synthetically generated independent 

 Gaussian sequences and sequences derived by sampling actual ocean 

 wave-force records obtained during hurricane conditions. The 

 simulation algorithms were derived using state-transition, 

 z-transform and Runge-Kutta methods. Through the use of Shannon 

 sampling expansion for bandlimited functions, a new type of state- 

 transition algorithm and a modification of the classical fourth- 

 order Runge-Kutta method were derived and shown to result in 

 increased accuracy over the methods currently in common use. 

 This is particularly noticeable for low sampling rates. 



16 



