Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials
نویسندگان
چکیده
In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials f1 and f2 in the differential indeterminate y with order one and arbitrary degree is given. That is, a non-singular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant of f1, f2, δf1, δf2 treated as polynomials in y, y , y is shown to be a non-zero multiple of the differential resultant of f1, f2. Although very special, this seems to be the first matrix representation for a class of nonlinear generic differential polynomials.
منابع مشابه
Linear sparse differential resultant formulas
Let P be a system of n linear nonhomogeneous generic sparse ordinary differential polynomials in n − 1 differential indeterminates. In this paper, differential resultant formulas are presented to compute, whenever it exists, the sparse differential resultant ∂Res(P) introduced by Li, Gao and Yuan in [12], as the determinant of the coefficient matrix of an appropriate set of derivatives of diffe...
متن کاملBernoulli matrix approach for matrix differential models of first-order
The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...
متن کاملViewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
متن کاملA new approach for solving the first-order linear matrix differential equations
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...
متن کاملOperational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...
متن کامل