Jacobi matrix differential equation, polynomial solutions, and their properties

Differential Polynomial Rings of Triangular Matrix Rings

Analytic properties of matrix Riccati equation solutions

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...

On the Polynomial Solutions of the Generalized Lame Differential Equation

According to Heine (see Marden [l, §9], or Marden [2]),1 there exist some choices F(z) of the polynomial R(z) corresponding to each of which equation (1.1) has a polynomial solution S(z). The 5(z) were called Stieltjes polynomials by Van Vleck in honor of the man who first studied the location of their zeros relative to those of P(z). For a similar reason, we shall call the F(z) Van Vleck polyn...

Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

Symmetric Matrix Polynomial Equation

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...