Algorithms for Changing the Step Size

Krogh, Fred T.

doi:10.1137/0710081

Cited by 72 publications

(23 citation statements)

References 6 publications

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“…As suggested by Shampine and Gordon, restrictions on ratio of successive step size is set to overcome convergence and stability issues of variable step size techniques. The step size algorithm from [9] for doubling or halving the step size which is implemented in a step size changing technique from [10] is applied to ensure stability.…”

Section: Explicit and Implicit Backward Differences Methodsmentioning

confidence: 99%

The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

Rasedee¹,

Suleiman²,

Ahmadian³

et al. 2016

Journal of Soft Computing and Applications

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In this article a variable order variable step size technique in backwards difference form is used to solve nonlinear Riccati differential equations directly. The method proposed requires calculating the integration coefficients only once at the beginning, in contrast to current divided difference methods which calculate integration coefficients at every step change. Numerical results will show that the variable order variable step size technique reduces computational cost in terms of total steps without effecting accuracy.

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Section: Explicit and Implicit Backward Differences Methodsmentioning

confidence: 99%

The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

Rasedee¹,

Suleiman²,

Ahmadian³

et al. 2016

Journal of Soft Computing and Applications

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“…Many methods have been examined for step-size alteration for ODEs [21]. In this application, it is desirable that the method employed can be implemented as simply as possible, and we either halve or double the step size, depending on whether the most recent sample was outside or inside a given tolerance , compared with the Adams prediction.…”

Section: B Varying the Sampling Ratementioning

confidence: 99%

Variable-rate data sampling for low-power microsystems using modified adams methods

Irvine

Wang

Dickman

et al. 2003

IEEE Trans. Signal Process.

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Abstract-A method for variable-rate data sampling is proposed for the purpose of low-power data acquisition in a small footprint microsystem. The procedure enables energy saving by utilizing dynamic power management techniques and is based on the Adams-Bashforth and Adams-Moulton multistep predictorcorrector methods for ordinary differential equations. NewtonGregory backward difference interpolation formulae and past value substitution are used to facilitate sample rate changes. It is necessary to store only 2 + 1 equispaced past values of and the corresponding values of , where = ( ), and is the number of steps in the Adams methods. For the purposes of demonstrating the technique, fourth-order methods are used, but it is possible to use higher orders to improve accuracy if required.Index Terms-Adams methods, dynamic power management, interpolation, low-power, variable-rate sampling.

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“…Krogh [6] discusses a number of ways to change the stepsize, but only two are seen in popular codes. One that applies to all LMMs is to use interpolation to obtain the values needed if we are to continue the integration with the constant stepsize formula (2.1) and the new stepsize.…”

mentioning

confidence: 99%

The Effect of Changing the Stepsize in Linear Multistep Codes

Shampine¹,

Bogacki²

1989

SIAM J. Sci. and Stat. Comput.

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In the usual convergence theory for linear multistep methods, a constant stepsize h is used. For a method of order p, the discretization error is proportional to h p+I. In a variable step code, it is necessary to predict what the discretization error would be if the stepsize were changed to rh. It is usual to say that the observed error will be altered by a factor of p+I. Unfortunately this is not correct for multistep methods. The discrepancy arises in the fact that the usual theory does not model the way variable stepsize codes actually work. In this paper the correct behavior is determined for important classes of formulas and ways of changing stepsize.

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Algorithms for Changing the Step Size

Cited by 72 publications

References 6 publications

The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

Variable-rate data sampling for low-power microsystems using modified adams methods

The Effect of Changing the Stepsize in Linear Multistep Codes

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