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High Order Finite Difference Schemes for the Solution of Elliptic PDEs

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Computational and Information Science (CIS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3314))

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Abstract

We solve nonlinear elliptic PDEs by stable finite difference schemes of high order on a uniform meshgrid. These schemes have been introduced in [1] in the class of Boundary Value Methods (BVMs) to solve two-point Boundary Value Problems (BVPs) for second order ODEs and are high order generalizations of classical finite difference schemes for the first and second derivatives. Numerical results for a minimal surface problem and for the Gent model in nonlinear elasticity are presented.

Work supported by GNCS and MIUR (60% project). The work of I. S. was partially supported by the Progetto Giovani Ricercatori Università di Lecce-MIUR 2001/2002.

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References

  1. Amodio, P., Sgura, I.: High order finite difference schemes for the solution of second order BVPs. J. Comput. Appl. Math. (2004) (in press)

    Google Scholar 

  2. Horgan, C., Saccomandi, G., Sgura, I.: A two-point boundary-value problem for the axial shear of hardening isotropic incompressible nonlinearly elastic materials. SIAM J. Appl. Math. 62 (2002) 1712–1727

    Article  MathSciNet  MATH  Google Scholar 

  3. Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer Series in Comput. Math., vol. 23. Springer, Berlin (1994)

    MATH  Google Scholar 

  4. Ascher, U., Mattheij, R., Russell, R.: Numerical Solution of Boundary Value Problems for ODEs. Classics in Applied Mathematics, vol. 13. SIAM, Philadelphia (1995)

    Google Scholar 

  5. Brugnano, L., Trigiante, D.: Solving ODEs by Linear Multistep Initial and Boundary Value Methods. Gordon & Breach, Amsterdam (1998)

    Google Scholar 

  6. Fornberg, B., Ghrist, M.: Spatial finite difference approximations for wave–type equations. SIAM J. Numer. Anal. 37, 105–130 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ge, L., Zhang, J.: Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients. J. Comput. Appl. Math. 143, 9–27 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari, 70125, Bari, Italy

    Pierluigi Amodio

  2. Dipartimento di Matematica, Università degli Studi di Lecce, 73100, Lecce, Italy

    Ivonne Sgura

Authors
  1. Pierluigi Amodio
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  2. Ivonne Sgura
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Editor information

Editors and Affiliations

  1. School of Electronic Science and Technology, Anhui University, Hefei, Anhui, China

    Jun Zhang

  2. College of Science, Donghua University, 1882 Yan’an Xilu Road, 20051, Shanghai, China

    Ji-Huan He

  3. BASICS, Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Yuxi Fu

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© 2004 Springer-Verlag Berlin Heidelberg

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Amodio, P., Sgura, I. (2004). High Order Finite Difference Schemes for the Solution of Elliptic PDEs. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_1

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  • DOI: https://doi.org/10.1007/978-3-540-30497-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24127-0

  • Online ISBN: 978-3-540-30497-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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