Wavelet-based adaptive grids for multirate partial differential-algebraic equations

2009 ◽  
Vol 59 (3-4) ◽  
pp. 495-506 ◽  
Author(s):  
A. Bartel ◽  
S. Knorr ◽  
R. Pulch
Keyword(s):  
Differential Algebraic Equations ◽  
Adaptive Grids ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Partial Differential Algebraic Equations

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

2018 ◽  
Vol 23 (3) ◽  
pp. 39 ◽  
Author(s):  
Chahid Ghaddar
Keyword(s):  
Method Of Lines ◽  
Differential Algebraic Equations ◽  
Least Square ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Seamless Integration ◽  
Partial Differential Algebraic Equations ◽  
The Method Of Lines ◽  
Mathematical Equations ◽  
Rapid Modeling

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.

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