Numerical algorithm research for nonlinear ODEs and stability analysis in computer

This paper discussed numerical algorithm of the initial and boundary value problem of nonlinear ordinary differential equations and analysis its stability in computer. The iterated algorithm with spline function for initial value problem in nonlinear ordinary differential equations was studied. Based on the principle of Newton´s algorithm for nonlinear equation, a parallel algorithm for initial value problems in nonlinear ordinary differential equations is constructed and then analysis the stability of this method. It shows that the methods have high precision and quick convergence speed and good stability.