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Convergence and Dynamics of a Higher-Order Method [PDF]
Symmetry, 2020 Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution.
Alejandro Moysi +5 more
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A maximal chain approach to topology and order
International Journal of Mathematics and Mathematical Sciences, 1988 On ordered sets (posets, lattices) we regard topologies (or, more general convergence structures) which on any maximal chain of the ordered set induce its own interval topology.
R. Vainio
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Order convergence and topological convergence [PDF]
Proceedings of the American Mathematical Society, 1965 In a complete lattice it is possible to define a notion of convergence (for arbitrary nets) known as order convergence (o-convergence) ; for definitions see [l,p.5°]and [3, p. 65]. As a general rule o-convergence is not a topological convergence; i.e., the lattice cannot be topologized so that nets o-converge if and only if they converge with respect ...
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Convergence Rate for the Ordered Upwind Method [PDF]
Journal of Scientific Computing, 2016 The Ordered Upwind Method (OUM) is used to approximate the viscosity solution of the static Hamilton-Jacobi-Bellman (HJB) with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution that converges to the exact solution, but no convergence rate has been theoretically proven.
Alex Shum +2 more
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Axioms, 2022 In this paper, we present a high-order approximate solution with uniform accuracy for nonlinear 3D Volterra integral equations. This numerical scheme is constructed based on the three-dimensional block cubic Lagrangian interpolation method.
Zi-Qiang Wang +2 more
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On the convergence of second-order spectra and multiplicity [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010 The notion of second-order relative spectrum of a self-adjoint operator acting on a Hilbert space has been studied recently in connection with the phenomenon of spectral pollution in the Galerkin method. In this paper we examine how the second-order spectrum encodes precise information about the multiplicity of the isolated eigenvalues of the ...
Boulton, L., Strauss, M.
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A Newton-like Midpoint Method for Solving Equations in Banach Space
Foundations, 2023 The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fréchet derivative.
Samundra Regmi +3 more
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Convergence of a second order Markov chain [PDF]
Applied Mathematics and Computation, 2014 16 pages, 3 ...
Sheng-Long Hu, Liqun Qi 0001
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Local convergence of a fifth convergence order method in Banach space
Arab Journal of Mathematical Sciences, 2017 We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative ...
Ioannis K. Argyros, Santhosh George
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On (Δm,I)-Statistical Convergence of Order α
The Scientific World Journal, 2014 The idea of I-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of (Δm,I)-statistical convergence of order α and strong (Δpm,I)-Cesàro ...
Mikail Et +2 more
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