Multiquadric quasi-interpolation methods for solving partial differential algebraic equations

Authors

  • Wendi Bao,

    1. Department of Computation and Applied Mathematics, College of Science, China University of Petroleum, Qingdao, People's Republic of China
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  • Yongzhong Song

    Corresponding author
    1. Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, Department of Information & Computational Sciences, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China
    • Correspondence to: Yongzhong Song, Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, People's Republic of China, (e-mail: yzsong@njnu.edu.cn)

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Abstract

In this article, we propose two meshless collocation approaches for solving time dependent partial differential algebraic equations (PDAEs) in terms of the multiquadric quasi-interpolation schemes. In presenting the process of the solution, the error is estimated. Furthermore, the comparisons on condition numbers of the collocation matrices using different methods and the sensitivity of the shape parameter c are given. With the use of the appropriate collocation points, the method for PDAEs with index-2 is improved. The results show that the methods have some advantages over some known methods, such as the smaller condition numbers or more accurate solutions for PDAEs which has an modal index-2 or an impulse solution with index-2. Copyright © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 95–119, 2014

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