Some General Linear Methods for the Numerical Solution of Non-Stiff IVPs in ODEs

In this paper, we consider the construction of explicit General Linear Methods (GLM) for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The discrete coefficients of the methods are obtained from the continuous coefficients of the continuo...

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Vydané v:Journal of algorithms & computational technology Ročník 7; číslo 1; s. 41 - 63
Hlavní autori: Okuonghae, R. I., Ikhile, M. N. O., Ogunleye, S. O.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: London, England SAGE Publications 01.03.2013
SAGE Publishing
Predmet:
Algorithms
Differential equations
Eigenvalues
Initial value problems
Interpolation
Mathematical models
Runge-Kutta method
Stability
boundary locus
General linear method
continuous order conditions
collocation and interpolation approach
ISSN:1748-3018, 1748-3026
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Popis
Shrnutí:In this paper, we consider the construction of explicit General Linear Methods (GLM) for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The discrete coefficients of the methods are obtained from the continuous coefficients of the continuous schemes which are derived using collocation and interpolation approach. One of the new method's stability matrix M(z) has a single nonzero eigenvalue similar to that of the third order Runge Kutta method (RKM), while other eigenvalues being zero, such general linear method is referred to as GLM with Runge Kutta stability. Numerical results are provided to illustrate the application of the new schemes. The new schemes are found to have competitive accuracy with the existing Almost Runge Kutta Methods (ARKM) discussed in Butcher [9].
Bibliografia:ObjectType-Article-2
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ISSN:1748-3018
1748-3026
DOI:10.1260/1748-3018.7.1.41