Efficient and accurate numerical solving of partial differential equations (PDE) is essential for many problems in science and engineering. In this paper we discuss spectral symplectic methods with different numerical accuracy on example of Nonlinear Schrodinger Equation (NLSE), which can be taken as a model for versatile kinds of conservative systems. First, second and fourth order approximation have been observed and reviewed considering execution speed vs. accuracy trade off. In order to utilize the possibility of modern hardware, the numerical algorithms are implemented both on CPU and GPU. Results are compared in sense of execution speed, single/double precision, data transfer and hardware specifications.


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