Characteristic-value problem: Difference between revisions

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|Meaning=A problem in which an undetermined [[parameter]] is involved in the  coefficients of a differential equation and in which the solution of the differential equation, with  associated [[boundary conditions]], exists only for certain discrete values of the parameter, called  [[eigenvalues]] (or characteristic values, sometimes principal values).
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|Explanation=An important example of a physical problem that leads to a characteristic-value problem is the  determination of the modes and frequencies of a vibrating system. In this case the [[dependent variable|dependent  variable]] of the differential equation represents the displacements of the system and the parameter  represents the frequencies of vibration.
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== characteristic-value problem ==
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<div class="definition"><div class="short_definition">A problem in which an undetermined [[parameter]] is involved in the  coefficients of a differential equation and in which the solution of the differential equation, with  associated [[boundary conditions]], exists only for certain discrete values of the parameter, called  [[eigenvalues]] (or characteristic values, sometimes principal values).</div><br/> <div class="paragraph">An important example of a physical problem that leads to a characteristic-value problem is the  determination of the modes and frequencies of a vibrating system. In this case the [[dependent variable|dependent  variable]] of the differential equation represents the displacements of the system and the parameter  represents the frequencies of vibration.</div><br/> </div>
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Latest revision as of 09:11, 26 March 2024

A problem in which an undetermined parameter is involved in the coefficients of a differential equation and in which the solution of the differential equation, with associated boundary conditions, exists only for certain discrete values of the parameter, called eigenvalues (or characteristic values, sometimes principal values).

An important example of a physical problem that leads to a characteristic-value problem is the determination of the modes and frequencies of a vibrating system. In this case the dependent variable of the differential equation represents the displacements of the system and the parameter represents the frequencies of vibration.

  1. In general, any quantity of a problem that is not an independent variable.
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