Families of methods for ordinary differential equations based on trigonometric polynomials

Neta, Beny; Ford, Chase

doi:10.1016/0377-0427(84)90066-9

Cited by 38 publications

(18 citation statements)

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“…' (h Ht> y (t n> • < 6 » Insertina (4) in (6) [13] developed Nystrom and generalized Milne-Simpson type methods. These methods showed less sensitivity to perturbation in w" but require the eigenvalues of the Jacobian to be purely imaainary.…”

Section: Distribution Statement (Of Thla Rapott)mentioning

confidence: 99%

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Special methods for problems whose oscillatory solution is damped

Neta

1989

Applied Mathematics and Computation

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Section: Distribution Statement (Of Thla Rapott)mentioning

confidence: 99%

“…PROJECT, TASK AREA 4 WORK UNIT NUMBERS II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE September 1986 14. MONITORING AGENCY NAME ft ADDRESSf// different from Controlling Office) 13.…”

mentioning

confidence: 99%

Special methods for problems whose oscillatory solution is damped

Neta

1989

Applied Mathematics and Computation

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“…Gautschi, 1961;Neta & Ford, 1984) y(t) + ( 100 + 4:2) y(t) = 0, 1 ::::; t ::::; 10, with the initial values according to the "almost" periodic particular solution…”

Section: Uncertainty In the Periodicitymentioning

confidence: 99%

“…This unfavourable property of the Gautschi methods (which are of Adams type, i.e. p(() = (k-(k-1 ) motivated Neta & Ford (1984) to propose methods of . These methods, however, although demonstrating a less sensitive behaviour if the value of w 0 is perturbed, are rather sensitive to non-imaginary noise (cf.…”

Section: Introductionmentioning

confidence: 99%

Linear Multistep Methods with Reduced Truncation Error for Periodic Initial-value Problems

Houwen¹,

Sommeijer²

1984

IMA Journal of Numerical Analysis

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A common feature of most methods for numerically solving ordinary differential equations is that they consider the problem as a standard one without exploiting specific properties the solution may have.Here we consider initial-value problems the solution of which is a priori known to possess an oscillatory behaviour. The methods are of linear multistep type and special attention is paid to decreasing the value of those terms in the local truncation error which correspond to the oscillatory solution components. Numerical results obtained by these methods are reported and compared with those obtained by the corresponding conventional linear multistep methods and by the methods developed by Gautschi.

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“…Special methods based on a-priori knowledge of the frequency were developed by Bettis [3], Steifel and Bettis [22], Gautschi [10], Neta and Ford [17], Neta [19], van der Houwen and Sommeijer [12], Lyche [14] and Sommeijer et al [21].…”

mentioning

confidence: 99%