【摘要】 该文阐述了求解两体问题的线性对称多步数值方法——Obrechkoff法。N体问题是一个很难的问题,只有少数微分方程存在解析解,近似方法是解微分方程的主要手段,高精度的轨道问题需要长时间的数值积分。因此,选用线性对称多步方法,在其主结构上增加高阶微商,不仅有理想的精度和较好的稳定性,而且可以大大减少截断误差,尤其在很大程度上减小了误差系数。研究表明,该方法求解两体问题的数值解具有高精度、高效率及稳定性好的优点。更多还原

【Abstract】 We focus on the new kind of P- stable Obrechkoff method for the numerical solution of orbital problems. However,only a few of these differential equations can be solved exactly. Approximate methods are the main means for solving,analyzing and understanding physics problems. Through improving the Wang’ s method,we develop a new kind of P- stable four- step Obrechkoff method by adding the higher- order derivatives. This proposed method is very effective but has very high local truncation error. The numerical experiments for the numerical solution of orbital problems has the advantage over the Wang’ s method in accuracy and efficiency.更多还原