On maximum norm contractivity of second order damped single step methods

I. Faragó, Mihály Kovács

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we consider A(θ)-stable finite difference methods for numerical solutions of dissipative partial differential equations of parabolic type. Combining two rational approximation methods with different orders of accuracy, where the lower order method is applied n0 times (n0 fixed) at each time step, we prove the existence of a second order method which is contractive for all time steps. Moreover, we shed light on the conditions on the lower order method which are sufficient (and sometimes necessary) to obtain the optimal order of accuracy. For the one-dimensional heat equation we construct a family of numerical methods which are contractive in the maximum norm for all values of the discretization parameters. We also present numerical examples to illustrate our results.

Original languageEnglish
Pages (from-to)91-108
Number of pages18
JournalCalcolo
Volume40
Issue number2
Publication statusPublished - 2003

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Contractivity
Maximum Norm
Finite difference method
Damped
Partial differential equations
Numerical methods
Rational Approximation
Approximation Methods
Heat Equation
Difference Method
Finite Difference
Partial differential equation
Discretization
Numerical Methods
Numerical Solution
Sufficient
Numerical Examples
Necessary
Hot Temperature

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On maximum norm contractivity of second order damped single step methods. / Faragó, I.; Kovács, Mihály.

In: Calcolo, Vol. 40, No. 2, 2003, p. 91-108.

Research output: Contribution to journalArticle

Faragó, I. ; Kovács, Mihály. / On maximum norm contractivity of second order damped single step methods. In: Calcolo. 2003 ; Vol. 40, No. 2. pp. 91-108.
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