SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER

First-Order Singular and Discontinuous Differential Equations

Bernoulli 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...

A method for solving first order fuzzy differential equation

Constructing Lie algebras of first order differential operators

We extend Guillemin and Sternberg’s Realization Theorem for transitive Lie algebras of formal vector fields to certain Lie algebras of formal first order differential operators, and show that Blattner’s proof of the Realization Theorem allows for a computer implementation that automatically reproduces many realizations derived in the existing literature, and that can also be used to compute new...

Singularities of the eta function of first-order differential operators

We report on a particular case of the paper [7], joint with Raphaël Ponge, showing that generically, the eta function of a first-order differential operator over a closed manifold of dimension n has first-order poles at all positive integers of the form n− 1, n− 3, n− 5, . . .. Version française abrégée Soit D la classe des operateurs différentiels elliptiques symmétriques d’ordre 1 sur une var...