Rapid convergence for telegraph systems with periodic boundary conditions
Summary: 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: \(\partial^{n - 1} F(t, x, U)/\partial U^{n - 1}\) 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 \(n\).
scientific article; zbMATH DE number 6816052