Interval versions of central-difference method for solving the Poisson equation in proper and directed interval arithmetic

DOI10.2478/fcds-2013-0009zbMath1328.65222OpenAlexW2148938981MaRDI QIDQ902736

Tomasz Hoffmann, Barbara Szyszka, Andrzej Marciniak

Publication date: 4 January 2016

Published in: Foundations of Computing and Decision Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/fcds-2013-0009

zbMATH Keywords

Poisson equationinterval methodsdirected interval arithmeticcentral-difference methodfloating-point interval arithmeticproper interval arithmetic

Mathematics Subject Classification ID

General methods in interval analysis (65G40) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (1)

Recursive solution of initial value problems with temporal discretization

Cites Work

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• NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
• An Interval Arithmetic Approach for the Construction of an Almost Globally Convergent Method for the Solution of the Nonlinear Poisson Equation on the Unit Square
• A numerical approach to the proof of existence of solutions for elliptic problems
• The Solution of Nonlinear Elliptic Dirichlet Problems on Rectangles by Almost Globally Convergent Interval Methods
• Almost Globally Convergent Interval Methods for Discretizations of Nonlinear Elliptic Partial Differential Equations

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