An improved precise Runge-Kutta integration

作者：Fu M^*; Liang H

来源：Acta Scientiarum Naturalium Universitatis Sunyatseni, 2009, 48(5): 1-5.

• Calculation technique of matrix exponential
• Nonlinear dynamical equation
• Numerical integration
• Precise time-step integration method
• Runge-Kutta integration

An improved precise Runge-Kutta integration is presented for solving nonlinear dynamical system. First of all, Newton-Cotes integral formula is used to calculate the special solution of nonhomogeneous equation in Duhamel integral form for linear system. Since a simple and convenient calculational method is advanced, the handling technique can reduce the whole gross of computation and storage comparing to common numerical integration methods with the same precision. Then the technique is extended to nonlinear system and unknown state parameters are forecasted consulting to the geometrical explanation of Runge-Kutta method. The method has better precision and efficiency to a relatively high extent than the existed precision Runge-Kutta method and the result of the numerical examples substantiates the availability adequately.

• 出版日期2009
• 单位中山大学