The efficiency of application of dual-processor computers, various operating systems, and library functions adapted to the used processors for increasing the execution speed of a computer program used for solving a system of two 3D nonlinear Schrödinger equations is analyzed. The computation speeds obtained on computers with 32-bit and 64-bit processors are compared. It is shown that the use of all mentioned possibilities and the Intel Itanium 2 processor provides from to threefold to tenfold total saving of time, depending on the operating system and the computer type. Parallelization of the algorithm for different operating systems in combination with the use of a library adapted to the processor can increase the program’s execution speed by a factor of 1.5–3.