Results 1 to 10 of about 1,096,545 (384)
Transforming Radical Differential Equations to Algebraic Differential Equations [PDF]
Mediterranean Journal of Mathematics, 2021 In this paper, we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations ...
Sebastian Falkensteiner, Rafael Sendra
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Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations [PDF]
arXiv, 2005 First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero. Combining with Fuchs' conditions for algebraic differential equations without movable critical point, an algorithm is ...
Guoting Chen, Yujie Ma
arxiv +3 more sources
On algebraic integrals of a differential equation
Discrete and Continuous Models and Applied Computational Science, 2019 We consider the problem of integrating a given differential equation in algebraic functions, which arose together with the integral calculus, but still is not completely resolved in finite form.
Mikhail D Malykh +2 more
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On algebraic solutions of Lamé's differential equation
Journal of Differential Equations, 1981 In two previous papers [ 1, 21 we reconsidered and improved Klein’s method for establishing whether a given second order linear differential equation with rational function coefficients (over an algebraic curve) has a full set of algebraic solutions.
F. Baldassarri
semanticscholar +4 more sources
Solutions of algebraic differential equations
Journal of Differential Equations, 1983 This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants.
Lee A. Rubel
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Algebraic and differential operator equations
Linear Algebra and its Applications, 1988 AbstractExplicit expressions for solutions of boundary-value problems and Cauchy problems related to the operator differential equation X(n)+An−1Xn−1)+⋯+A0X=0 are given in terms of solutions of the algebraic operator equation Xn+An−1Xn−1 +⋯+A0=0. A method for solving this algebraic equation is studied.
L. Jódar
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Numerical solution to Volterra integro-differential equations using collocation approximation [PDF]
Mathematics and Computational Sciences, 2023 This paper considers the collocation method for the numerical solution of the Volterra integro- differential equation using polynomial basis functions.
Ganiyu Ajileye, Sikiru Amoo
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Singularities of algebraic differential equations [PDF]
Advances in Applied Mathematics, 2021 There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of ordinary or partial differential equations.
Lange-Hegermann, Markus +3 more
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Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian [PDF]
AUT Journal of Mathematics and Computing, 2022 It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton’s method. Newton’s method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution ...
Mohammad Ali Mehrpouya
doaj +1 more source
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers [PDF]
ACM Transactions on Mathematical Software, 2020 In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures.
D. J. Gardner +3 more
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