Abstract. Observability of a general nonlinear system—given in terms of an ODE ẋ = f(x) and an output map y = c(x)—is defined as in linear system theory (i.e. if f(x) = Ax and c(x) = Cx). In contrast to standard treatment of the subject we present a criterion for observability which is not a generalization of a known linear test. It is obtained by evaluation of “approximate first integrals”. Th...

In past decades, the optimal control of distributed parameter system had been received much more attention in academic field. A wide spectrum of problems in applications can be solved by methods of optimal control, such as chemical engineering and vehicle dynamics. Modern optimal control theories and applied models are not only represented by ODE, but also by PDE, especially nonlinear parabolic...

This paper discusses possible solving strategies regarding four ODE problems, all relevant and currently out of the scope of the Maple ODE solver. The problems are: 1. Transformations linearizing non-linear first order ODEs 2. Non-linear 2nd order ODEs for which point symmetries are of no use 3. Hypergeometric solutions for 2nd order linear ODEs 4. Solutions for third and higher order linear OD...

Boundary feedback control for a coupled nonlinear PDE-ODE system (in the two and three dimensional cases) is studied. Particular focus is put on the monodomain equations arising in the context of cardiac electrophysiology. Neumann as well as Dirichlet based boundary control laws are obtained by an algebraic operator Riccati equation associated with the linearized system. Local exponential stabi...

A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

introduced in this inquiry and review is a balladry which exists both in divan of hassan ghaznavi and attar. in addition, the existing differences between the two also revealed balladry, and some lines in this ode were corrected according to divan of hassan ghaznavi. it is very important to note that the opening sixteen lines of this ode, except for the 7th and 8th lines, have been attributed t...

Numerical methods are important in computational neuroscience where complex nonlinear systems are studied. This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integro-differential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficien...