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**Numerical solution of differential algebraic equations using a multiquadric approximation scheme.**
*(English)*
Zbl 1217.65161

Summary: The objective of this paper is to solve differential algebraic equations using a multiquadric approximation scheme. Therefore, we present the notation and basic definitions of the Hessenberg forms of the differential algebraic equations. In addition, we present the properties of the proposed multiquadric approximation scheme and its advantages, which include using data points in arbitrary locations with arbitrary ordering. Moreover, error estimation and the run time of the method are also considered. Finally some experiments were performed to illustrate the high accuracy and efficiency of the proposed method, even when the data points are scattered and have a closed metric.

### MSC:

65L80 | Numerical methods for differential-algebraic equations |

### Keywords:

multiquadric approximation scheme; differential algebraic equations; Hessenberg forms of differential algebraic equations; error estimation; run time of the method; scattered data points
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\textit{S. K. Vanani} and \textit{A. Aminataei}, Math. Comput. Modelling 53, No. 5--6, 659--666 (2011; Zbl 1217.65161)

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### References:

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