Galerkin method for the determination of periodic and quasiperiodic solutions of nonlinear systems of differential equations (Q796718)

For the vector differential equation (1) \(dx(t)/dt=X(t,x(t))\) in which the right hand-side is 2\(\pi\)-periodic in t a modification of Galerkin method for determining periodic and quasi-periodic solutions is suggested. This modification is able to accelerate the convergence of the Galerkin approximation to exact solutions. The author investigates the dependence between the approximation convergence speed and the smoothness of the right-hand side of system (1).