In this paper an infinite-dimensional LQR control-based design for a system containing linear hyperbolic partial differential equations coupled with linear ordinary differential equations is presented. The design is based on an infinite-dimensional Hilbert state-space representation of the coupled system. The feedback control gain is obtained by solving algebraic and differential matrix Riccati...

and Applied Analysis 3 to a class of complex matrix equations with conjugate and transpose of the unknowns. Jonsson and Kågström 24, 25 proposed recursive block algorithms for solving the coupled Sylvester matrix equations and the generalized Sylvester and Lyapunov Matrix equations. Very recently, Huang et al. 26 presented a finite iterative algorithms for the one-sided and generalized coupled ...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

We develop an overlapping block preconditioner based on an additive Schwarz method for preconditioning the system of equations arising from discretizing the shallow water equations using the spectral ocean element method approach. The system is complicated by being sparse, but having a very large number of nonzeroes in any row of the matrix, which is never stored. The resulting coupled system o...

Continuous-time nonlinear stochastic differential state and measurement equations, all of which have coefficients capable of abrupt changes at a random time, are considered; finite-state jump Markov chains are used to model the changes. Conditional probability densities, which are essential in obtaining filtered estimates for these hybrid systems, are then derived. They are governed by a couple...

Coupled modified nonlinear Schrödinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initialboundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x, t) and v(x, t) of CMNLS equations are exists, and we show that it can be expre...

We study the attractor mechanism for N = 1 supergravity coupled to vector and chiral multiplets and compute the attractor equations of these theories. These equations may have solutions depending on the choice of the holomorphic symmetric matrix f ΛΣ which appears in the kinetic lagrangian of the vector sector. Models with non trivial electric-magnetic duality group which have or have not attra...

A computationally efficient numerical method for the solution of nonlinear sea ice dynamics models employing viscous-plastic rheologies is presented. The method is based on a semi-implicit decoupling of the x and y ice momentum equations into a form having better convergence properties than the coupled equations. While this decoupled form also speeds up solutions employing point relaxation meth...