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Papageorgiou, George; Famelis, Ioannis Th.; Tsitouras, Ch.

doi:10.1023/a:1016644726305

Cited by 26 publications

(3 citation statements)

References 7 publications

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“…These include Runge‐Kutta, Runge‐Kutta‐Nyström, finite differences, or other multistep methods and especially four‐step methods and six‐step ones . A number of these methods follow some kind of fitting (eg, phase, trigonometric, or exponential) or share a special propery (eg, P‐stability) …”

Section: Preliminary Discussionmentioning

confidence: 99%

Local interpolants for Numerov‐type methods and their implementation in variable step schemes

Медведев

Simos

Tsitouras

2019

Math Methods in App Sciences

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The classical explicit fourth-order Numerov-type method is considered. The equations of condition for deriving the corresponding interpolants are given.Then using a local error estimation, we may construct a stable variable step scheme. Applying this new implementation in a set of problems, we get very pleasant results. KEYWORDS explicit hybrid Numerov, variable step, ′′ = (x, ) MSC CLASSIFICATION 65L05; 65L06 PRELIMINARY DISCUSSIONWe are interested in the special form of the initial value problem (IVP) of second-orderwith ∶ R × R m → R m and 0 , ′ 0 ∈ R m . Here, y ′ is not present in (1). Math Meth Appl Sci. 2019;42:7047-7058. wileyonlinelibrary.com/journal/mma

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Section: Preliminary Discussionmentioning

confidence: 99%

Local interpolants for Numerov‐type methods and their implementation in variable step schemes

Медведев

Simos

Tsitouras

2019

Math Methods in App Sciences

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“…Tol being the tolerance selected by the user, and 9 10 a safety factor. If Est n+1 < Tol, then the step is accepted, and we continue with the procedure by performing local extrapolation, meaning that the more accurate approximation will be used to advance the integration.…”

Section: Basic Conceptsmentioning

confidence: 99%

“…The class of Runge-Kutta-Nyström (RKN) codes has been usually considered to obtain approximate solutions to problem (1). Regarding such usage, different methods of the class of diagonally implicit RKN methods have been studied by Sommeijer in [1], Van der Houwen and Sommeijer in [2], Imoni et al in [3], Sharp et al in [4], Senu et al in [5][6][7][8], Papageorgiou et al in [9], Al-khasawneh et al in [10], and Ismail et al in [11]. In this study, we develop a new efficient 5(4) diagonally implicit RKN method (DIRKN) in variable step-size to solve the problem in (1).…”

Section: Introductionmentioning

confidence: 99%

Development of an Efficient Diagonally Implicit Runge–Kutta–Nyström 5(4) Pair for Special Second Order IVPs

Demba

Senu

Ramos

et al. 2022

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In this work, a new pair of diagonally implicit Runge–Kutta–Nyström methods with four stages is constructed. The proposed method has been derived to solve initial value problems of special second-order ordinary-differential equations. The principal local truncation error of the new method is obtained, and the main characteristics of the new method are analyzed. Some numerical experiments are performed, which demonstrate the robustness and efficiency of the new embedded pair.

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Interpolants for sixth‐order Numerov‐type methods

Alolyan

Simos

Tsitouras

2019

Math Methods in App Sciences

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The classical four-stage family of explicit sixth-order Numerov-type method is considered. We provide two kinds of interpolants: (a) a three-step interpolation based on all available data at mesh points and (b) a local interpolant (ie, two steps) that is constructed after solving scaled equations of condition. These latter equations are explained and provided here. Applying these interpolants in a set of tests, we conclude that they produce global errors of the same magnitude with the underlying method. KEYWORDSy ′′ = f(x, y), explicit hybrid Numerov, interpolation MSC CLASSIFICATION 65L05; 65L06Math Meth Appl Sci. 2019;42:7349-7358.wileyonlinelibrary.com/journal/mma

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Cited by 26 publications

References 7 publications

Local interpolants for Numerov‐type methods and their implementation in variable step schemes

Local interpolants for Numerov‐type methods and their implementation in variable step schemes

Development of an Efficient Diagonally Implicit Runge–Kutta–Nyström 5(4) Pair for Special Second Order IVPs

Interpolants for sixth‐order Numerov‐type methods

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