Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method.
Smoothers and their applications in autonomous system theory.
Smoothness as an invariant property of coefficients of linear differential equations
Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.
Solution formelle Gevrey d'une équation singulièrement perturbée : le cas multidimensionnel
Nous considérons les équations différentielles possédant un paramètre de contrôle, singulièrement perturbées par un petit paramètre . Nous prouvons alors, par des techniques de majoration directe, que les solutions formelles et le paramètre de contrôle sont des séries Gevrey en .
Solution of some plane filtration problems with partially unknown boundaries.
Solutions series for some non-harmonic motion equations.
Solving Differential Equations by Parallel Laplace Method with Assured Accuracy
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006We produce a parallel algorithm realizing the Laplace transform method for the symbolic solving of differential equations. In this paper we consider systems of ordinary linear differential equations with constant coefficients, nonzero initial conditions and right-hand parts reduced to sums of exponents with polynomial coefficients.
Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension.
Some properties of linear homogeneous transformation of independent variable in ordinary differential linear equations
Some properties of solutions to polynomial systems of differential equations.
Some relations satisfied by Hermite-Hermite matrix polynomials
The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite...
Stationary groups of linear differential equations
Stokes multipliers for subdominant solutions of second order differential equations with polynomial coefficients.
Sturmian theory and transformations for the Riccati equation
Summation of Formal Power Series Through Iterated Laplace Integrals.
Sur des fonctions de deux variables provenant de l'inversion des intégrales de deux fonctions données
Sur la théorie des équations différentielles linéaires
Sur le méthode de l'intégrale généralisée de Laplace appliquée aux équations aréolaires linéaires
Sur le théorème de comparaison entre cohomologies de De Rham algébrique et -adique rigide
Soit un fibré vectoriel à connexion sur une courbe algébrique lisse définie sur le corps de nombres algébriques. On démontre qu’il y a équivalence entre le théorème de Clark sur la convergence de séries formelles solutions d’une équation différentielle d’exposants nombres non-Liouville et l’isomorphisme entre la cohomologie de de Rham algébrique du fibré et la cohomologie de de Rham du fibré -adique associé sur la courbe -adique rigide associée.