[00816] Ultraspherical spectral methods for time-dependent problems
Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
Type : Contributed Talk
Abstract : Spectral methods solve elliptic partial differential equations (PDEs) numerically. Their main advantage is spectral convergence, i.e., error decays exponentially when the solution is analytic. We present numerical schemes for solving some time-dependent linear PDEs utilizing the ultraspherical spectral method in space and time, thus portraying overall spectral convergence. Moreover, they lead to sparse and well-conditioned linear systems. We compare their performance with existing spectral schemes and explore their parallelization in time.
