Systems of second-order linear ODE’s with constant coefficients and their symmetries II The case of non-diagonal coefficient matrices
نویسنده
چکیده
We complete the analysis of the symmetry algebra L for systems of n second-order linear ODEs with constant real coefficients, by studying the case of coefficient matrices having a non-diagonal Jordan canonical form. We also classify the Levi factor (maximal semisimple subalgebra) of L, showing that it is completely determined by the Jordan form. A universal formula for the dimension of the symmetry algebra of such systems is given. As application, the case n = 5 is analyzed.
منابع مشابه
Finding the Best Coefficients in the Objective Function of a Linear Quadratic Control Problem
Finding the best weights of the state variables and the control variables in the objective function of a linear-quadratic control problem is considered. The weights of these variables are considered as two diagonal matrices with appropriate size and so the objective function of the control problem becomes a function of the diagonal elements of these matrices. The optimization problem which is d...
متن کاملSequential second derivative general linear methods for stiff systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this p...
متن کاملSeepage with Nonlinear Permeability by Least Square FEM
In seepage problems, the coefficients of permeability in Laplace equation are usually assumed to be constant vs. both space and time; but in reality these coefficients are variable. In this study, the effect of material deformation due to external loads (consolidation) and variation of head in the consolidation process are considered. For the first case, formulation of kx and ky can be defined ...
متن کاملThe Symmetries of Equivalent Lagrangian Systems and Constants of Motion
In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to th...
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کامل