SPURIOUS RESONANCE IN SEMIDISCRETE METHODS FOR THE KORTEWEG–DE VRIES EQUATION
A multiple scales analysis of semidiscrete methods for the Korteweg–de Vries equation is conducted. Methods that approximate the spatial derivatives by finite differences with arbitrary order accuracy and the limiting method, the Fourier pseudospectral method, are considered. The analysis reveals th...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2014-01, Vol.52 (6), p.2863-2882 |
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| container_title | SIAM journal on numerical analysis |
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| creator | FASONDINI, M. SCHOOMBIE, S. W. |
| description | A multiple scales analysis of semidiscrete methods for the Korteweg–de Vries equation is conducted. Methods that approximate the spatial derivatives by finite differences with arbitrary order accuracy and the limiting method, the Fourier pseudospectral method, are considered. The analysis reveals that a resonance effect can occur in the semidiscrete solution but not in the solution of the continuous equation. It is shown for the Fourier pseudospectral discretization that resonance can only be caused by aliased modes. The spurious semidiscrete solutions are investigated in numerical experiments and we suggest methods for avoiding spurious resonance. |
| doi_str_mv | 10.1137/130947143 |
| format | Article |
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The spurious semidiscrete solutions are investigated in numerical experiments and we suggest methods for avoiding spurious resonance.</description><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Constraining</subject><subject>Derivatives</subject><subject>Discretization</subject><subject>Fictitious names</subject><subject>Finite difference methods</subject><subject>Fourier analysis</subject><subject>Harmonics</subject><subject>Integers</subject><subject>Linearization</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Numerical analysis</subject><subject>Ordinary differential equations</subject><subject>Spectral methods</subject><subject>Zero</subject><issn>0036-1429</issn><issn>1095-7170</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNo9kL1OwzAcxC0EEqUw8ABIHmEI-O_YcTJWqdtGtDHkA8bIdRypVUtK3A5svANvyJMQVMTdcDrppxsOoWsg9wC-eACfREwA80_QAEjEPQGCnKIBIX7gAaPRObpwbk36HoI_QCp_KrNElTnOZK7SURpLnKQ4l4tknORxJguJF7KYqXGOJyrDxUziR5UV8lVOvz-_xhK_ZInMsXwuR0Wi0kt01uiNs1d_OUTlRBbxzJuraRKP5p6hjO29gHLdRKYOrOB1rU1dhzqwBkJqRMOjPmgNlHBBrRFLWEYQhqzRQmjNaiaMP0S3x91d174frNtX25UzdrPRb7Y9uAoCDoz7Ue8hujuipmud62xT7brVVncfFZDq97Tq_7SevTmya7dvu3-QMg60l_8Dbfxh1g</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>FASONDINI, M.</creator><creator>SCHOOMBIE, S. 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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Approximation Boundary conditions Constraining Derivatives Discretization Fictitious names Finite difference methods Fourier analysis Harmonics Integers Linearization Mathematical analysis Mathematical models Numerical analysis Ordinary differential equations Spectral methods Zero |
| title | SPURIOUS RESONANCE IN SEMIDISCRETE METHODS FOR THE KORTEWEG–DE VRIES EQUATION |
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