We propose generalizations of two numerical algorithms to solve the system of linearly coupled nonlinear Schrödinger equations (NLSEs) describing the propagation of light pulses in multi-core optical fibers. An iterative compact dissipative second-order accurate in space and fourth-order accurate in time scheme is the first numerical method. This compact scheme has strong stability due to inclusion of the additional dissipative term. The second algorithm is a generalization of the split-step Fourier method based on Padé approximation of the matrix exponential. We compare a computational efficiency of both algorithms and show that the compact scheme is more efficient in terms of performance for solving a large system of coupled NLSEs. We also present the parallel implementation of the numerical algorithms for shared memory systems using OpenMP.