In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from well known traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain th...

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we des...

The purpose of the talk is to give a review on effective methods for the numerical solution of hyperbolic systems with parabolic relaxation. We consider mathematical models described by a set of hyperbolic equations with relaxation. As the relaxation parameter vanishes, the characteristic speeds of the system diverge, and the system reduces to a parabolic-type equation (typically a convection-d...

Phosphorylation is thought to be an essential first step in the prompt deactivation of photoexcited rhodopsin. In vitro, the phosphorylation can be catalyzed either by rhodopsin kinase (RK) or by protein kinase C (PKC). To investigate the specific role of RK, we inactivated both alleles of the RK gene in mice. This eliminated the light-dependent phosphorylation of rhodopsin and caused the singl...

In this paper we present a high-order accurate cell-centered finite volume method for the semi-implicit discretization of multidimensional hyperbolic systems in conservative form on unstructured grids. This method is based on a special splitting of the physical flux function into a convective and a non-convective part. The convective contribution to the global flux is treated implicitly by mimi...

A new composite Runge–Kutta (RK) method is proposed for semilinear partial differential equations such as Korteweg–de Vries, nonlinear Schrödinger, Kadomtsev– Petviashvili (KP), Kuramoto–Sivashinsky (KS), Cahn–Hilliard, and others having high-order derivatives in the linear term. The method uses Fourier collocation and the classical fourth-order RK method, except for the stiff linear modes, whi...