Library Planning for Automation

Crank-Nicholson techniqueIBM 7094 II digital computer.In all cases the step-size chosen with the Runge-Kutta method was taken to be as large as possible to just maintain stability.The equations were solved to at least 4 figure accuracy in all cases.It is seen that the proposed method is significantly faster than the Runge-Kutta and faster than the standard Crank-Nicholson method in this example.It should be noted, however, that the storage space required in using the proposed method is greater than in using more conventional techniques.Approximately 5« 2 words (where n is the order of the matrix A) are required for the case that n is large with the proposed method as compared to the n 2 words required in the case of the Runge-Kutta method.