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Tracing complex singularities with spectral methods
https://www.sciencedirect.com/science/article/pii/0021999183900451
Tracing Complex Singularities with Spectral Methods - NASA/ADS
https://ui.adsabs.harvard.edu/abs/1983JCoPh..50..138S/abstract
A numerical method for investigating the possibility of blow-up after a finite time is introduced for a large class of nonlinear evolution problems. With initial data analytic in the space variable(s), the solutions have for any t > 0 complex-space singularities at the edge of an analyticity strip of width δ( t) Loss of regularity corresponds to the vanishing of δ( t). Numerical ...
Study of Complex Singularities by Filtered Spectral Method
https://journals.jps.jp/doi/abs/10.1143/JPSJ.55.1542
A filtered spectral method is proposed for the study of the distribution in the complex-space of singularities of solutions to partial differential equations. It is applied to the Burgers equation to trace the motion in the complex-space of the singularities close to the real axis in the processes of shock-formation and collision of two shocks.
Sulem C Sulem PL Frisch H 1983 Tracing complex …
https://www.coursehero.com/file/p1np8uma/Sulem-C-Sulem-PL-Frisch-H-1983-Tracing-complex-singularities-with-spectral/
Sulem C Sulem PL Frisch H 1983 Tracing complex singularities with spectral. Sulem c sulem pl frisch h 1983 tracing complex. School Memorial University of Newfoundland; Course Title ENGI 3424; Uploaded By cynthiakate54321. Pages 45 This preview shows page 43 - 45 out of 45 pages.
Study of Complex Singularities by Filtered Spectral Method
https://ui.adsabs.harvard.edu/abs/1986JPSJ...55.1542K/abstract
A filtered spectral method is proposed for the study of the distribution in the complex-space of singularities of solutions to partial differential equations. It is applied to the Burgers equation to trace the motion in the complex-space of the singularities close to the real axis in the processes of shock-formation and collision of two shocks.
Computing the Dynamics of Complex Singularities of Nonlinear …
https://epubs.siam.org/doi/abs/10.1137/S1111111102398305
A two-step strategy is proposed for the computation of singularities in nonlinear PDEs. The first step is the numerical solution of the PDE using a Fourier spectral method; the second step involves numerical analytical continuation into the complex plane using the epsilon algorithm to sum the Fourier series. Test examples include the inviscid Burgers and nonlinear heat …
EVOLUTION OF COMPLEX SINGULARITIES AND KOLMOGOROV …
https://link.springer.com/chapter/10.1007/1-4020-4181-0_36
Part of the Fluid Mechanics and Its Applications book series (FMIA,volume 79) Abstract The analyticity strip method is used to trace complex singularities in direct numerical simulations of the Taylor-Green flows, performed with up to 2048 3 collocation points. No indication of finite-time real singularity is found.
(PDF) Deciphering Singularities by Discrete Methods
https://www.researchgate.net/publication/242922502_Deciphering_Singularities_by_Discrete_Methods
PDF | We consider the problem of estimating numerically the parameters of singularities of solutions of differential equations. We propose a novel... | Find, read and cite all the research you ...
Detection of complex singularities for a function of ... - UCLA …
https://www.math.ucla.edu/~caflisch/Pubs/Pubs2013-2014/SiegelSingularityDetectionIMA2013.pdf
Implementation of the method of Sulem et al. typically involves high-resolution (spectral) numer- ical computation of a time-evolution problem, and δ(t) and other properties of the nearest complex singularity are determined from asymptotic behaviour of the Fourier transform.
COMPUTING THE DYNAMICS OF COMPLEX SINGULARITIES …
http://appliedmaths.sun.ac.za/~weideman/SING/singpde2.pdf
Step 1: Use a numerical method to solve the PDE up to a time near breakdown. Step 2: Then use numerical analytic continuation to extend the computed solution into the complex plane. In the rst step we use the Fourier spectral method for the space discretization, combined with a method-of-lines integration with respect to the time variable. We
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