Two-parameter Sturm-Liouville problems

This paper deals with the computation of the eigenvalues of two-parameter Sturm- Liouville (SL) problems using the Regularized Sampling Method, a method which has been effective in computing the eigenvalues of broad classes of SL problems (Singular, Non-Self-Adjoint, Non-Local, Impulsive,...). We have shown, in this work that it can tackle two-parameter SL problems with equal ease. An example was provided to illustrate the effectiveness of the method.Comment: 9 page

Input-Output Maps for Nonlinear Systems, Fractional Integration and Rational Representations

In this paper we shall make a systematic use of the fractional integration operator to derive input-output maps in compact form for linear and bilinear systems and general autonomous nonlinear systems. This will enable us to obtain simple rational approximations to input-output maps

Computation of the Eigenpairs of Two-Parameter Sturm-Liouville Problems Using the Regularized Sampling Method

This paper deals with the computation of the eigenvalues of two-parameter Sturm-Liouville (SL) problems using the Regularized Sampling Method, a method which has been effective in computing the eigenvalues of broad classes of SL problems (singular, non-self-adjoint, nonlocal, impulsive, etc.). We have shown, in this work that it can tackle two-parameter SL problems with equal ease. An example was provided to illustrate the effectiveness of the method

Rational Expansion for Nonlinear Input-Output Maps

This paper introduces a Rational Expansion for Nonlinear Input-Output MAPS. The method is new and is based on the rational expansion of functions of several complex variables. If truncated, this series reduces to a ratio of truncated Volterra series, A "feedback form" will be presented

A Functional Expansion and Stability for Nonlinear Input-Output Maps.

In this paper we shall use the global bilinearization of a linear analytic system using the tensor operator approach introduced in (6). We shall generalize the result on finite dimensional bilinear systems (13) to this class of systems. We use the idea of diagonal dominance for tensor operators to derive an exponential stability result. Few examples will be presentd to illustrate the theory

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Darcian natural convection in an inclined trapezoidal cavity partly filled with a porous layer and partly with a nanofluid layer

The problem of Darcian natural convection in a trapezoidal cavity partly filled with porous layer and partly with nanofluid layer is studied numerically using finite difference method. The left slopping wall is maintained at a constant hot temperature and the right slopping wall is maintained at a constant cold temperature, while the horizontal walls are adiabatic. Water-based nanofluids with Ag or Cu or TiO2 nanoparticles are chosen for the investigation. The governing parameters of this study are the Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10–5 ≤ Da ≤ 10–3), nanoparticle volume fraction (0 ≤ φ ≤ 0.2), porous layer thickness (0.3 ≤ S ≤ 0,7), the side wall inclination angle (0° ≤ ϕ ≤ 21.8°) and the inclination angle of the cavity (0° ≤ ϖ ≤ 90°). Explanation for the influence of various above-mentioned parameters on streamlines, isotherms and overall heat transfer is provided on the basis of thermal conductivities of nanoparticles, water and porous medium. It is shown that convection increases remarkably by the addition of silver-water nanofluid and the heat transfer rate is affected by the inclination angle of the cavity variation. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems

Computing eigenvalues of regular Sturm-Liouville problems

AbstractIn this paper, we shall extend our results on the use of sampling theory in the computation of the Dirichlet eigenvalues of regular Sturm-Liouville problems to problems with more general separable boundary conditions

Optimal control of nonlinear systems: A recursive approach

AbstractIn this paper, we shall generalize our result [1] on the optimal control of bilinear systems to nonlinear systems. Adomian's decomposition is used to derive series expansions of the optimal control and state