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Math. Comput. Appl. 2018, 23(3), 39; https://doi.org/10.3390/mca23030039

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

ExcelWorks LLC, Sharon, MA 02067, USA
Received: 10 July 2018 / Revised: 1 August 2018 / Accepted: 1 August 2018 / Published: 3 August 2018
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Abstract

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. View Full-Text
Keywords: partial differential algebraic equations; parameter estimation; dynamical optimization; Excel spreadsheet; PDE; nonlinear programming partial differential algebraic equations; parameter estimation; dynamical optimization; Excel spreadsheet; PDE; nonlinear programming
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Ghaddar, C.K. Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm. Math. Comput. Appl. 2018, 23, 39.

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