Sergey Shindin

Jacek Banasiak, Luke O. Joel, Sergey Shindin

In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations.

J. Banasiak, L. O. Joel, S. Shindin

In this paper, we prove that for a large class of growth-decay-fragmentation problems the solution semigroup is analytic and compact and thus has the Asynchronous Exponential Growth property.

Sergey Shindin, Nabendra Parumasur, Olabisi Aluko

In the paper, we study approximation properties of the Malmquist-Takenaka-Christov (MTC) system. We show that the discrete MTC approximations converge rapidly under mild restrictions on functions asymptotic at infinity. This makes them particularly suitable for solving semi- and quasi-linear problems containing Fourier multipliers, whose symbols are not smooth at the origin. As a concrete application, we provide rigorous convergence and stability analyses of a collocation MTC scheme for solving the nonlinear Benjamin equation. We demonstrate that the method converges rapidly and admits an efficient implementation, comparable to the best spectral Fourier and hybrid spectral Fourier/finite-element methods described in the literature.