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Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm

机译:基于功能电子表格范例的偏微分代数方程组的快速建模和参数估计

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We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort.
机译:我们提出了一种系统化的电子表格方法,用于建模和优化通用偏微分代数方程(PDAE)。该方法采用了纯电子表格PDAE求解器功能设计,该设计封装了“线法”,并允许与Excel电子表格非线性编程求解器无缝集成。在具有间断特性和耦合时间导数的复杂参数化PDAE系统上,设计并论证了两种备选的最小二乘动态最小化方案。应用该方法仅涉及定义一些与原始数学方程式非常相似的公式,而无需任何编程技能。它为需要非常规编程技能和精力的更复杂环境提供了一种更简单的替代方法。

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