The nonlinear Dirac equation is an important model in quantum physics
with a set of conservation laws and a multi-symplectic formulation. In this paper, we
propose energy-preserving and multi-symplectic wavelet algorithms for this model.
Meanwhile, we evidently improve the efficiency of these algorithms in computations
via splitting technique and explicit strategy. Numerical experiments are conducted
during long-term simulations to show the excellent performances of the proposed algorithms
and verify our theoretical analysis.