Computational speed when the array dimension is large

The 4th-order Runge-Kutta numerical method is applied to drive the time-domain responses of a second order differential equation, where the unknown motion is a function of time. I find that the speed of the operation drops dramatically when my simulation time becomes longer. How can I improve the speed of the program? I compared calculation speed between 200s and 7200s simulation time and the drop in running speed was noticeable. The length of all variables are pre-defined before the loop.The simulated time step is 0.01s, and the computer processor is "Intel Xeon W-2295, 18 Cores, 36 Threads, 3.0GHz, 4.8GHz Turbo" and the memory is 64GB (4*16GB) DDR4-2933 REG ECC.

[James Tursa]

Please post the differential equation you are solving and the code you are using. It is very hard to suggest improvements without seeing these details.

Answer 1

[Steven Lord]

Have you tried a stiffer solver? See this post on Cleve Moler's blog for more information about stiffness.