RESEARCH ON HIGH ORDER SINGLE STEP METHOD TO SOLVE NONLINEAR DYNAMIC EQUATIONS

This paper conducts research on the applicability of high order step method to solve nonlinear dynamic equations ?(t)=G(Z,t)Z(t)+H(t). Based on the Taylor series expansion, the prediction formulas are proposed, making the high order step method to an implicit method. Combining the implicit method and the predict-correct method, the nonlinear dynamic equations can be solved. Another way to solve the nonlinear dynamic equations is to transform the presented equations to the equations ?(t)=GZ(t)+H(Z,t), from which a new implicit high order step method is derived. The nonlinear dynamic equations can be solved by the presented method. Numerical examples demonstrate the effectiveness of these two solutions. This paper extends the application scope of the high order single step method.