Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions. (13th November 2017) - Wang, Peiguang; Liu, Xiang
Abstract : The generalized quasilinearization method is applied in this paper to a telegraph system with periodic boundary conditions. We consider the case in which the forcing function F ( t, x, U ) satisfies the following condition: ∂ n - 1 F ( t, x, U ) / ∂ U n - 1 exists and is quasimonotone nondecreasing or nonincreasing. We develop nonlinear iterates of order n - 1 which will be different with n being even or odd. Finally, we develop two sequences which converge to the solution of the telegraph system and the convergence is of order n .