This file contains three sections of discussions to supplement the main text. The first section has a brief introduction to matrix and vector notation for those unfamiliar to such notation. (Use of this notation allows a concise representation of the system of differential equations used by this report.) The second section gives the full set of differential equation system for the model, and gi...

There are only a few analytic solutions available for this partial differential equation. Schrödinger found all of the most useful ones in his first paper on Quantum Mechanics: the Coulomb potential and the harmonic oscillator potential. He published the solution to the nonrelativistic Coulomb problem in his first Wave Mechanics paper but solved the relativistic problem six months earlier. He a...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

To understand the solution of a linear, time-invariant differential-algebraic equation (DAE), one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left half-plane), the solution can exhibit transient growth before its inevitable decay. When the equation results from the linearization of a nonlinear system, this transient...

In this paper, with the aim of estimating internal dynamics matrix of a gimbaled Inertial Navigation system (as a discrete Linear system), the discretetime Hamilton-Jacobi-Bellman (HJB) equation for optimal control has been extracted. Heuristic Dynamic Programming algorithm (HDP) for solving equation has been presented and then a neural network approximation for cost function and control input ...

Abstract We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type flu...

, Abstract. This paper is concerned with the derivation of open-loop 8tackelberg (OL8) solutions of a class of continuoustime two-player nonzero-sum differential games characterized by quadratic cost functionals and linear singular systems. By applying the calculus of variations, necessary conditions are derived under which the op~n-Ioop 8tackelberg solution of the leader exists. Under the tran...

In the present work, certain aspects, restricted to the visual system, of the J. Gonzalo’s research, are interpreted according to a simple linear theory of time-dispersion applied to the dynamic cerebral system, characterized by its excitability and its reaction velocity.

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...