The Property of Finality and the Analysis of Problems in Reactor Space-Time Kinetics by Various Modal Expansions

Kaplan, S.

doi:10.13182/nse61-a25887

Cited by 48 publications

(27 citation statements)

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“…The splitting of D must be T done in such a way that A 1 and A 2 are diagonally dominant and A 1 +A 1 T and A 2 + 2 are negative definite. The ratio of the time step size to the square of the spatial mesh spacings was assumed to be fixed, although no limit was placed on the size of this ratio.…”

Section: Stabilitymentioning

confidence: 99%

Finite Difference Techniques for the Solution of the Reactor Kinetics Equations.

Reed¹,

Kent²

1969

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A class of finite difference methods called splitting techniques are presented for the solution of the multigroup diffusion theory reactor kinetics equations in two space dimensions. A subset of the above class is shown to be consistent with the differential equations and numerically stable. An exponential transformation of the semi-discrete equations is shown to reduce the truncation error of the above methods so that they beoome practical methods for two-dimensional problems. A variety of numerical experiments are presented which illusthate the truncation error, convergence rates, and stability of a particular member of the above class.

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Section: Stabilitymentioning

confidence: 99%

Finite Difference Techniques for the Solution of the Reactor Kinetics Equations.

Reed¹,

Kent²

1969

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“…Starting from a given initial state (7,0), the differential equation (13) generally perinits the construction of many possible solutions.…”

Section: A Definitions and Notations 33mentioning

confidence: 99%

Control and Stability Analysis of Spatially Dependent Nuclear Reactor Systems.

Hsu¹

1967

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“…Since the fundamental mode and the first few harmonics contribute most to the flux distribution the series expansion for the Laplace transformed flux will be truncated a s follows: Now the following inequalities must all be satisfied for stability of the perturbed flux a s given by equation (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24).…”

Section: (5-22)mentioning

confidence: 99%

Xenon-135 Induced Instabilities of the Neutron Flux in Nuclear Reactors

Sandquist¹

1964

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The Property of Finality and the Analysis of Problems in Reactor Space-Time Kinetics by Various Modal Expansions

Cited by 48 publications

References 1 publication

Finite Difference Techniques for the Solution of the Reactor Kinetics Equations.

Finite Difference Techniques for the Solution of the Reactor Kinetics Equations.

Control and Stability Analysis of Spatially Dependent Nuclear Reactor Systems.

Xenon-135 Induced Instabilities of the Neutron Flux in Nuclear Reactors

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