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A method for approximate solution of initial value and spectral problems forone dimensional Dirac equation based on an analytic approximation of thetransmutation operator is presented. In fact the problem of numericalapproximation of solutions is reduced to approximation of the potential matrixby a finite linear combination of matrix valued functions related togeneralized formal powers introduced in arXiv:1904.03361. Convergence rateestimates in terms of smoothness of the potential are proved. The method allowsone to compute both lower and higher eigendata with an extreme accuracy.

Analytic approximation of transmutation operators for one-dimensional  stationary Dirac operators and applications to solution of initial value and  spectral problems