Parallel Solution of Transient Problems by Trapezoidal Integration

The numerical method presented in this paper permits the solution of differential equations by trapezoidal integration in a time of order log2 T, where T is the number of discrete time steps required for the solution. The number of required parallel processors is T/2. Linear and nonlinear examples are presented. The nonlinear example corresponds to a small stability problem. The classical trapezoidal integration algorithm is compared to the new parallel trapezoidal algorithm in terms of solution time requirements. Also, for the nonlinear example the comparison includes the number of iterations and convergence characteristics. Overall conclusions indicate that the parallel algorithm is always much faster and sometimes has better convergence characteristics. Potential limitations of the method are also discussed.