Interval Difference Methods for Solving the Poisson Equation

Andrzej Marciniak; Tomasz Hoffmann

doi:10.1007/978-3-319-75647-9_21

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Title

Interval Difference Methods for Solving the Poisson Equation

Authors

Andrzej Marciniak (WI) ^{[ 1 ][ 2.3 ][ P ]}
Tomasz Hoffmann

^{[ 1 ]} Instytut Informatyki, Wydział Informatyki, Politechnika Poznańska | ^{[ P ]} employee

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication

2018

Chapter type

chapter in monograph / paper

Publication language

english

Keywords

EN

interval difference methods
floating-point interval arithmetic
Poisson’s equation
boundary value problem in partial differential equations

Abstract

EN In the paper we resemble interval difference method of second order designed by us earlier and present new, fourth order interval difference methods for solving the Poisson equation with Dirichlet boundary conditions. Interval solutions obtained contain all possible numerical errors. Numerical solutions presented confirm the fact that the exact solutions are within the resulting intervals.

Pages (from - to)

259 - 270

DOI

10.1007/978-3-319-75647-9_21

URL

https://link.springer.com/chapter/10.1007/978-3-319-75647-9_21

Book

Differential and Difference Equations with Applications ICDDEA, Amadora, Portugal, June 2017

Presented on

International Conference on Differential & Difference Equations and Applications (ICDDEA 2017), 5-9.06.2017, Amadora, Portugal

Ministry points / chapter

20