Approximate solution of a nonlinear periodic boundary value problem (Q1090086)

The authors discuss the numerical solution of the following boundary value problem \(\dot x+f(t,x,\dot x)=0,\) \(x(0)=x(1)\). The authors discretize this equation by the usual difference scheme \(x_{i+1}=x_ i-hf(t_ i,x_ i,(x_{i+1}-x_ i)/h,\) \(x_ 0=x_ N\), \(i=0,1,...,N- 1\), where \(t_ i=ih\), \(i=0,1,...,N\), \(Nh=1\), and solve this system by iteration. They prove that this method is stable and convergent and give error estimates. The paper is illustrated by numerical examples.