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Multiquadric quasi‐interpolation methods for solving partial differential algebraic equations
Author(s) -
Bao Wendi,
Song Yongzhong
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21797
Subject(s) - mathematics , partial derivative , collocation (remote sensing) , interpolation (computer graphics) , orthogonal collocation , partial differential equation , collocation method , algebraic number , mathematical analysis , differential equation , ordinary differential equation , computer science , animation , computer graphics (images) , machine learning
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