Rational Approximation to Solutions of Linear Differential Equations with Algebraic Coefficients
نویسندگان
چکیده
منابع مشابه
Linear Differential Algebraic Equations with Constant Coefficients
Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are...
متن کاملExact solutions of linear equations with rational coefficients
An algorithm for computing the exact solutions of linear equations with rational coefficients, and its computer implementation, were described in [1].1 The basic idea of the algorithm is to convert the original system of equations into a system of congruences modulo various primes Pi, and combining the solutions by a procedure suggested by the Chinese Remainder Theorem. This process is continue...
متن کاملLinear Stochastic Differential-algebraic Equations with Constant Coefficients
We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue mea...
متن کاملLiouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Let L(y) = b be a linear differential equation with coefficients in a differential field K. We discuss the problem of deciding if such an equation has a non-zero solution in K and give a decision procedure in case K is an elementary extension of the field of rational functions or is an algebraic extension of a transcendental liouvillian extension of the field of rational functions. We show how ...
متن کاملRational solutions of Riccati differential equation with coefficients rational
This paper presents a simple and efficient method for determining the solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (E l) : y = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ + θ 2 = r, by reducing the number of check to be made and by accelerating the sea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.2307/2039996