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