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On the Stability of a Variable Step Exponential Splitting Method for Solving Multidimensional Quenching-Combustion Equations

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Modern Mathematical Methods and High Performance Computing in Science and Technology

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 171))

Abstract

This paper concerns the numerical stability of a splitting scheme for solving the three-dimensional degenerate quenching-combustion equation. The diffusion-type nonlinear equation possess highly nonlinear source terms, and is extremely important to the study of numerical combustions. Arbitrary fixed nonuniform spatial grids, which are not necessarily symmetric, are considered in our investigation. The numerical solution is advanced through a semi-adaptive exponential splitting strategy. The temporal adaptation is achieved via a suitable arc-length monitoring mechanism. Criteria for preserving the linear numerical stability of the decomposition method is proven under the spectral norm. A new stability criterion is proposed.

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Authors and Affiliations

  1. Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, One Bear Place, Waco, TX, 76798-7328, USA

    Joshua L. Padgett & Qin Sheng

Authors
  1. Joshua L. Padgett
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  2. Qin Sheng
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Corresponding author

Correspondence to Qin Sheng .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Raj Kumar Goel Institute of Technology, Ghaziabad, Uttar Pradesh, India

    Vinai K. Singh

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H.M. Srivastava

  3. Dipartimento di Matematica, University of Turin, Torino, Italy

    Ezio Venturino

  4. High Performance Computing Center (HLRS), University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Michael Resch

  5. Department of Mathematics, Netaji Subhas Institute of Technology, New Delhi, India

    Vijay Gupta

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Padgett, J.L., Sheng, Q. (2016). On the Stability of a Variable Step Exponential Splitting Method for Solving Multidimensional Quenching-Combustion Equations. In: Singh, V., Srivastava, H., Venturino, E., Resch, M., Gupta, V. (eds) Modern Mathematical Methods and High Performance Computing in Science and Technology. Springer Proceedings in Mathematics & Statistics, vol 171. Springer, Singapore. https://doi.org/10.1007/978-981-10-1454-3_13

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