On solving periodically perturbed nonconservative systems with a one-parameter embedding
The paper is concerned with solving the periodically perturbed nonconservative systems, which will be differentiably imbedded into an one-parameter family of operators. The solution of the systems is then found by continuing the solution curve of operator homotopy. When the Newton-Kantorovich's procedure is applied to the corresponding operator equations, an efficient algorithm is derived. Furthermore, the suitable condition on the optimum step size of the parameter is provided for assuring that the approximation solution will converge to the unique solution of the nonlinear periodically boundary value problem. Finally, the theoretical results are in excellent agreement with the numerical examples.
one-parameter embedding convergence nonlinear systems periodic solutions