Two-step Runge-Kutta Methods with Quadratic Stability Functions

We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions. We will aim for methods which are A -stable and L -stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to ei...

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Bibliographic Details
Published inJournal of scientific computing Vol. 44; no. 2; pp. 191 - 218
Main Authors Conte, D., D’Ambrosio, R., Jackiewicz, Z.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2010
Springer Nature B.V
Subjects
Algorithms
Computation
Computational Mathematics and Numerical Analysis
Construction
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Runge-Kutta method
Stability
Theoretical
Quadratic stability polynomials
Order conditions
Two-step Runge-Kutta methods
Absolute stability
stability
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Summary:We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions. We will aim for methods which are A -stable and L -stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-010-9378-x