Publication detail

Convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations

REBENDA, J. ŠMARDA, Z.

Original Title

Convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations

Czech Title

Konvergenční analýza iterativního schématu pro řešení počáteční ho problému muldidimensionálních parciálních diferenciálních rovnic

English Title

Convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations

Type

journal article

Language

en

Original Abstract

Existence and uniqueness of solutions of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations are proved using Banach fixed-point theorem. An iterative scheme is derived and rigorous convergence analysis of this scheme and an error estimate are included as well.

Czech abstract

Existence a jednoznačnost řešení počáteční úlohy pro jisté třídy muldimensionálních lineárních a nelineárních parciálních diferenciálních rovnic je dokázána pomocí Banachovy věty o pevném bodu. Je odvozeno iterativní schéma a je popsána konvergenční analýza této metody včetně odhadu chybydané metody.

English abstract

Existence and uniqueness of solutions of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations are proved using Banach fixed-point theorem. An iterative scheme is derived and rigorous convergence analysis of this scheme and an error estimate are included as well.

Keywords

Partial differential equation; Banach fixed-point theorem; Iterative scheme; Convergence analysis; Error estimate

RIV year

2015

Released

01.10.2015

Pages from

1772

Pages to

1780

Pages count

9

URL

BibTex


@article{BUT116953,
  author="Josef {Rebenda} and Zdeněk {Šmarda}",
  title="Convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations",
  annote="Existence and uniqueness of solutions of initial value problem for certain classes of multidimensional
linear and nonlinear partial differential equations are proved using Banach fixed-point theorem. An iterative scheme is derived and rigorous convergence analysis of this scheme and an error estimate are included as well.",
  chapter="116953",
  doi="10.1016/j.camwa.2015.07.018",
  howpublished="online",
  number="8",
  volume="2015 (70)",
  year="2015",
  month="october",
  pages="1772--1780",
  type="journal article"
}