Department Colloquium: The Fourier pseudo-spectral numerical schemes for nonlinear PDEs and their stability

Speaker: Cheng Wang, Professor, Department of Mathematics, University of Massachusetts Dartmouth

Abstract: The Fourier pseudo-spectral numerical schemes are considered for nonlinear partial differential equations (PDE). Stability and convergence analysis are analyzed in detail, such as viscous Burgers’ equation and incompressible fluid equations. Related applications to the incompressible quasi-geostrophic equation will also be addressed, in both 2-D and 3-D, for smooth and vortex sheet initial data. In addition, high order time-stepping schemes (up to fourth-order accuracy order) will be explored in detail. Unconditional stability is established for the implicit time-stepping algorithms.

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