Combination Of One-dimensional Hyperbolic Equations Difference Quotient And Its Promotion In The Two-dimensional

In this paper, I design a series of high-efficiency serial schemes and parallel algorithms for one-dimension and two-dimension hyperbolic equation.Firstly, a new kind of explicit difference scheme for one-dimension hyperbolic equation is proposed. The truncation error of the scheme is of ordero(τ~4 + h~4) .Secondly, a class of group parallel algorithms(GE,GEL,GER) containing biparameters are constructed for solving the hyperbolio equation u_t + au_x = 0. Thelocal truncation error is always of order o(τ+ h) ,The stability condition is r > 0withβ=1,1- 4/r~2<α<1 The stability condition is r>0 and r≠1 withβ=1,1-4/r~2 =α< 1. The local truncation error is of order o(τ~2 + h~2) withα= 1/2,β=(r-1)/(2r), The stability condition is 0 < r≤4/3 withα=1/2,β= (r-1)/(2r). In the end,a class of group parallel algorithms(GE,GEL,GER) are constructed for solving the two-dimensional hyperbolio equation u_t + au_x +bu_y=0 in this paper. The localtruncation error is always of order o(τ+ h) ,The stability condition is 0 < r≤1. Inthis paper, every type scheme is given numerical compute, and the result validates the theory analysis.In this paper, the difference schemes are better than those of before at precise and stability.