The viscosity method for the implicit double midpoint rule with numerical results and its applications

DOI10.1007/s40314-019-0811-yzbMath1438.47134OpenAlexW2919614465WikidataQ128267140 ScholiaQ128267140MaRDI QIDQ2322423

Shrijana Dhakal, Wutiphol Sintunavarat

Publication date: 4 September 2019

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-019-0811-y

zbMATH Keywords

strong convergencefixed pointnonexpansive mappingvariational inequality problemviscosity methodimplicit midpoint rulereal Hilbert space

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Applications of operator theory to differential and integral equations (47N20) Numerical solutions to equations with nonlinear operators (65J15) Fixed-point iterations (47J26)

Related Items (1)

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Cites Work

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• Asymptotic expansions of the global error for the implicit midpoint rule (stiff case)
• A semi-implicit mid-point rule for stiff systems of ordinary differential equations
• On solving certain nonlinear partial differential equations by accretive operator methods
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• The implicit midpoint rule for nonexpansive mappings
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• Convergence theorems for sequences of nonlinear operators in Banach spaces
• Iterative Algorithms for Nonlinear Operators
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• Implicit Midpoint Rule to the Nonlinear Degenerate Boundary Value Problems
• Viscosity Solutions of Minimization Problems
• EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR EQUATIONS OF EVOLUTION
• Fixed points of nonexpanding maps

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