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A simple and non-iterative numerical approach for solving high-order nonlinear ODEs

Conference Paper


Abstract


  • Although there are many numerical solution approaches

    to ordinary differential equations (ODEs) in the literature,

    very few are effective in solving non-linear ODEs, particularly

    when they are of order higher than one. With the

    modern symbolic calculation packages, such as Maple and

    Mathematica, being readily available in scientific research

    and engineering calculations, a new numerical method

    based on the repeated use of a symbolic calculation package

    is presented in this talk. Our method is particularly

    suitable for solving high-order nonlinear ODEs arising

    from initial value problems. One important feature of

    our approach is that there is no iteration required in the

    time marching process.

Publication Date


  • 2003

Citation


  • Zhu, S. (2003). A simple and non-iterative numerical approach for solving high-order nonlinear ODEs. In R. Moore (Eds.), International Congress on Industrial and Applied Mathematics (pp. 242-251). Sydney: ICIAM Management Committee.

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/768

Start Page


  • 242

End Page


  • 251

Place Of Publication


  • Sydney

Abstract


  • Although there are many numerical solution approaches

    to ordinary differential equations (ODEs) in the literature,

    very few are effective in solving non-linear ODEs, particularly

    when they are of order higher than one. With the

    modern symbolic calculation packages, such as Maple and

    Mathematica, being readily available in scientific research

    and engineering calculations, a new numerical method

    based on the repeated use of a symbolic calculation package

    is presented in this talk. Our method is particularly

    suitable for solving high-order nonlinear ODEs arising

    from initial value problems. One important feature of

    our approach is that there is no iteration required in the

    time marching process.

Publication Date


  • 2003

Citation


  • Zhu, S. (2003). A simple and non-iterative numerical approach for solving high-order nonlinear ODEs. In R. Moore (Eds.), International Congress on Industrial and Applied Mathematics (pp. 242-251). Sydney: ICIAM Management Committee.

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/768

Start Page


  • 242

End Page


  • 251

Place Of Publication


  • Sydney