Applied and Computational Mathematics

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Volume 2, Issue 4, August 2013

  • Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils

    Taras A. Dauzhenka, Igor A. Gishkeluk

    Issue: Volume 2, Issue 4, August 2013
    Pages: 100-108
    Received: 30 May 2013
    Published: 10 August 2013
    DOI: 10.11648/j.acm.20130204.11
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    Abstract: Consistency of the Douglas – Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applie... Show More
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  • Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method

    Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar

    Issue: Volume 2, Issue 4, August 2013
    Pages: 109-114
    Received: 5 August 2013
    Published: 30 August 2013
    DOI: 10.11648/j.acm.20130204.12
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    Abstract: In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the i... Show More
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