论文标题
使用光谱投影仪和重新计算的时间变化的半差分差异方程来求解时变的半明星差分方程的组合方法和重新计算
Combined numerical methods for solving time-varying semilinear differential-algebraic equations with the use of spectral projectors and recalculation
论文作者
论文摘要
获得了两种求解时间变化的半星化差异方程（DAE）的组合数值方法。证明了方法的收敛性和正确性。在构造方法时，可以使用数字发现的时变光谱投影仪。这使得无需其他分析转换即可以数值以原始形式求解DAE。为了提高第二种方法的准确性，使用重新计算。开发的方法适用于DAE的连续非线性部分，该部分可能不会在时间上差异，并且对全局Lipschitz条件的类型的限制不用于DAE全局溶解性和方法的收敛性。这扩展了方法的范围。实现全局可溶性定理条件可确保在任何给定时间间隔中存在独特的精确解决方案，这使得在任何时间间隔都可以寻求近似解决方案。提供了说明该方法能力及其在各种情况下的有效性的数值示例。为了证明这一点，考虑了电路动力学的数学模型。结果表明，这些模型的理论和数值分析的结果是一致的。
Two combined numerical methods for solving time-varying semilinear differential-algebraic equations (DAEs) are obtained. The convergence and correctness of the methods are proved. When constructing the methods, time-varying spectral projectors which can be found numerically are used. This enables to numerically solve the DAE in the original form without additional analytical transformations. To improve the accuracy of the second method, recalculation is used. The developed methods are applicable to the DAEs with the continuous nonlinear part which may not be differentiable in time, and the restrictions of the type of the global Lipschitz condition are not used in the presented theorems on the DAE global solvability and the convergence of the methods. This extends the scope of methods. The fulfillment of the conditions of the global solvability theorem ensures the existence of a unique exact solution on any given time interval, which enables to seek an approximate solution also on any time interval. Numerical examples illustrating the capabilities of the methods and their effectiveness in various situations are provided. To demonstrate this, mathematical models of the dynamics of electrical circuits are considered. It is shown that the results of the theoretical and numerical analyses of these models are consistent.
