Extended domain for fifth convergence order schemes
Cubo, 2021 We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations.
Ioannis K. Argyros, Santhosh George
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On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics [PDF]
, 2015 In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry.
Baur +4 more
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Extending the solvability of equations using secant-type methods in Banach space
Journal of Numerical Analysis and Approximation Theory, 2021 We extend the solvability of equations dened on a Banach space using numerically ecient secant-type methods. The convergence domain of these methods is enlarged using our new idea of restricted convergence region.
Ioannis K. Argyros, Santhosh George
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Enhancing Equation Solving: Extending the Applicability of Steffensen-Type Methods
Mathematics, 2023 Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods.
Ramandeep Behl +2 more
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Numerical solution of the simple Monge–Ampère equation with nonconvex dirichlet data on non-convex domains [PDF]
, 2017 The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampere equation is known independently of the convexity of the domain or Dirichlet boundary data - when the Monge-Ampere equation is posed as a Bellman ...
Jensen, Max
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Semi-local convergence of Cordero's sixth-order method
AIMS Mathematics<abstract><p>In this paper, the semi-local convergence of the Cordero's sixth-order iterative method in Banach space was proved by the method of recursion relation. In the process of proving, the auxiliary sequence and three increasing scalar functions can be derived using Lipschitz conditions on the first-order derivatives.
Xiaofeng Wang, Ning Shang
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Median evidential c-means algorithm and its application to community detection [PDF]
, 2015 Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical ...
Liu, Zhun-Ga +3 more
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SIR - an Efficient Solver for Systems of Equations
, 2017 The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. Since publication, SIR has proven robustness for a great variety of problems.
Lindvall, Kristoffer, Scheffel, Jan
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Multigrid waveform relaxation for the time-fractional heat equation [PDF]
, 2017 In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the ...
Gaspar, Francisco J., Rodrigo, Carmen
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Multistep Iterative Methods for Solving Equations in Banach Space
MathematicsThe novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius
Ramandeep Behl +4 more
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