【摘 要】
：
微分求积法和单步块方法都是单步多级数值方法,但是直接应用于求解非线性动力方程时的计算量比较巨大,为此提出了一种基于单步块方法的改进精细积分单步方法.结合精细积分法,该方法采用s级的单步块方法的第s个方程对Duhamel积分项进行数值积分.具体采用四阶Runge-Kutta法获得待求变量的预估值,并采用新四点积分公式计算Duhamel积分项.相对于现有的单步方法,该改进算法在数值精度和稳定性上更优.通过非线性动力方程的典型算例验证了该算法的优势.
【机 构】
：
攀枝花学院数学与计算机学院,四川攀枝花617000;国网上海市电力公司特高压换流站分公司,上海201413;国网四川省电力公司内江供电公司,四川内江641000;三峡大学电气与新能源学院,湖北宜昌44
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微分求积法和单步块方法都是单步多级数值方法,但是直接应用于求解非线性动力方程时的计算量比较巨大,为此提出了一种基于单步块方法的改进精细积分单步方法.结合精细积分法,该方法采用s级的单步块方法的第s个方程对Duhamel积分项进行数值积分.具体采用四阶Runge-Kutta法获得待求变量的预估值,并采用新四点积分公式计算Duhamel积分项.相对于现有的单步方法,该改进算法在数值精度和稳定性上更优.通过非线性动力方程的典型算例验证了该算法的优势.
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