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1.
  • Nordström, Jan, 1953-, et al. (author)
  • An explicit Jacobian for Newton's method applied to nonlinear initial boundary value problems in summation-by-parts form
  • 2024
  • In: AIMS Mathematics. - : AIMS Press. - 2473-6988. ; 9:9, s. 23291-23312
  • Journal article (peer-reviewed)abstract
    • We derived an explicit form of the Jacobian for discrete approximations of a nonlinear initial boundary value problems (IBVPs) in matrix-vector form. The Jacobian is used in Newton's method to solve the corresponding nonlinear system of equations. The technique was exemplified on the incompressible Navier-Stokes equations discretized using summation-by-parts (SBP) difference operators and weakly imposed boundary conditions using the simultaneous approximation term (SAT) technique. The convergence rate of the iterations is verified by using the method of manufactured solutions. The methodology in this paper can be used on any numerical discretization of IBVPs in matrix-vector form, and it is particularly straightforward for approximations in SBP-SAT form.
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2.
  • Schiebold, Cornelia (author)
  • Noncommutative AKNS systems and multisoliton solutions to the matrix sine-Gordon equation
  • 2009
  • In: Discrete and Continuous Dynamical Systems. - : American Institute of Mathematical Sciences (AIMS). - 1078-0947 .- 1553-5231. ; :Suppl, s. 678-690
  • Journal article (peer-reviewed)abstract
    • The main result is a very general solution formula for the noncommutative AKNS system, extending work by Bauhardt and P¨oppe. As anapplication, we construct for the matrix sine-Gordon equation N-soliton solutions analogous to the multisoliton solutions for the KdV equation due toGoncharenko.
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3.
  • Sorooshian, Shahryar, 1980, et al. (author)
  • Performance of the decision-making trial and evaluation laboratory
  • 2023
  • In: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
  • Journal article (peer-reviewed)abstract
    • Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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