Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions
Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sperling, L. [verfasserIn] |
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| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1986 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1986 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer-Verlag, 1965, 59(1986), 3-4 vom: Juni, Seite 183-200 |
|---|---|
| Übergeordnetes Werk: |
volume:59 ; year:1986 ; number:3-4 ; month:06 ; pages:183-200 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF01181663 |
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| Katalog-ID: |
OLC2030107107 |
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| 520 | |a Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. | ||
| 650 | 4 | |a Covariance | |
| 650 | 4 | |a Fluid Dynamics | |
| 650 | 4 | |a White Noise | |
| 650 | 4 | |a Spectral Density | |
| 650 | 4 | |a Covariance Function | |
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10.1007/BF01181663 doi (DE-627)OLC2030107107 (DE-He213)BF01181663-p DE-627 ger DE-627 rakwb eng 530 VZ Sperling, L. verfasserin aut Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions 1986 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1986 Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. Covariance Fluid Dynamics White Noise Spectral Density Covariance Function Enthalten in Acta mechanica Springer-Verlag, 1965 59(1986), 3-4 vom: Juni, Seite 183-200 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:59 year:1986 number:3-4 month:06 pages:183-200 https://doi.org/10.1007/BF01181663 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_2333 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4700 AR 59 1986 3-4 06 183-200 |
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10.1007/BF01181663 doi (DE-627)OLC2030107107 (DE-He213)BF01181663-p DE-627 ger DE-627 rakwb eng 530 VZ Sperling, L. verfasserin aut Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions 1986 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1986 Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. Covariance Fluid Dynamics White Noise Spectral Density Covariance Function Enthalten in Acta mechanica Springer-Verlag, 1965 59(1986), 3-4 vom: Juni, Seite 183-200 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:59 year:1986 number:3-4 month:06 pages:183-200 https://doi.org/10.1007/BF01181663 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_2333 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4700 AR 59 1986 3-4 06 183-200 |
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10.1007/BF01181663 doi (DE-627)OLC2030107107 (DE-He213)BF01181663-p DE-627 ger DE-627 rakwb eng 530 VZ Sperling, L. verfasserin aut Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions 1986 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1986 Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. Covariance Fluid Dynamics White Noise Spectral Density Covariance Function Enthalten in Acta mechanica Springer-Verlag, 1965 59(1986), 3-4 vom: Juni, Seite 183-200 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:59 year:1986 number:3-4 month:06 pages:183-200 https://doi.org/10.1007/BF01181663 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_2333 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4700 AR 59 1986 3-4 06 183-200 |
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10.1007/BF01181663 doi (DE-627)OLC2030107107 (DE-He213)BF01181663-p DE-627 ger DE-627 rakwb eng 530 VZ Sperling, L. verfasserin aut Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions 1986 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1986 Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. Covariance Fluid Dynamics White Noise Spectral Density Covariance Function Enthalten in Acta mechanica Springer-Verlag, 1965 59(1986), 3-4 vom: Juni, Seite 183-200 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:59 year:1986 number:3-4 month:06 pages:183-200 https://doi.org/10.1007/BF01181663 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_2333 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4700 AR 59 1986 3-4 06 183-200 |
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10.1007/BF01181663 doi (DE-627)OLC2030107107 (DE-He213)BF01181663-p DE-627 ger DE-627 rakwb eng 530 VZ Sperling, L. verfasserin aut Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions 1986 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1986 Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. Covariance Fluid Dynamics White Noise Spectral Density Covariance Function Enthalten in Acta mechanica Springer-Verlag, 1965 59(1986), 3-4 vom: Juni, Seite 183-200 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:59 year:1986 number:3-4 month:06 pages:183-200 https://doi.org/10.1007/BF01181663 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_31 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_2333 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4700 AR 59 1986 3-4 06 183-200 |
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approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions |
| title_auth |
Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions |
| abstract |
Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. © Springer-Verlag 1986 |
| abstractGer |
Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. © Springer-Verlag 1986 |
| abstract_unstemmed |
Summary The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations. © Springer-Verlag 1986 |
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Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions |
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