Galerkin alternating-direction method for a kind of three-dimensional nonlinear hyperbolic problems

A kind of three-dimensional nonlinear hyperbolic equation is firstly transformed into a first-order system of equations, then the Galerkin alternating-direction procedure for the system is derived. The error estimates of the procedure in H1H1 norm and L2L2 norm, respectively, are obtained by using the theory and techniques of priori estimate of differential equations. The numerical experiment is also given to support the theoretical analysis. Comparing the results of numerical example with the theoretical analysis, they are coincided.