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A class of efficient quadrature-based predictor–corrector methods for solving nonlinear systems

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  • Howk, Cory L.

Abstract

We extend a class of quadrature-based predictor–corrector techniques for root-finding to multivariate systems. They are found to have a rate of convergence of 1+2 regardless of the degree of precision for the quadrature technique from which they are derived, provided it is at least one. By reusing the linear system from the previous iterate, this class incorporates a significant improvement in computational time relative to the standard class through the inclusion of an LU-decomposition during the iteration. Complexity is equivalent to Newton’s Method, as they only require knowledge of F(x) and F′(x).

Suggested Citation

  • Howk, Cory L., 2016. "A class of efficient quadrature-based predictor–corrector methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 394-406.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:394-406
    DOI: 10.1016/j.amc.2015.12.032
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    References listed on IDEAS

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    1. Howk, Cory L., 2015. "Convergence of a class of efficient quadrature-based predictor–corrector methods for root-finding," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 189-200.
    2. Ullah, Malik Zaka & Serra-Capizzano, Stefano & Ahmad, Fayyaz, 2015. "An efficient multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with ODEs," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 249-259.
    3. Ullah, Malik Zaka & Serra-Capizzano, S. & Ahmad, Fayyaz & Al-Aidarous, Eman S., 2015. "Higher order multi-step iterative method for computing the numerical solution of systems of nonlinear equations: Application to nonlinear PDEs and ODEs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 972-987.
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