In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs). Maple's robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and the analytic Jacobian. The algorithm and implementation were found to be robust and efficient for index-1 DAE problems and scales well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solves the same in few seconds.

翻译：在本文中,一些适应性的单步方法,如Trapezoid(TR)、Inbillit-mid点(IMP)、Euler- backward(EB)和Radau IIA(Rad)方法,在Maple实施,以解决指数-1非线性差异代谢(DAEs)的指数-一非线性差异代谢(DAEs)方法。Maple在列表/集中搜索的强大和高效能力被利用来识别聚度模式和分析Jacobian。在指数-1 DAE问题和尺度方面,算法和运用得既健全又有效,对于系统大小高达10,000个非线性DAE的两维模型的有限差异/无限元素分解,并在几秒钟内解决同样的问题。