GEOMETRIC AND ALGEBRAIC PROPERTIES OF FIRST-ORDER DIFFERENTIAL EQUATIONS ON SMOOTH FINITE-DIMENSIONAL REAL MANIFOLDS

Differential - Algebraic Systems as Differential Equations on Manifolds

Based on the theory of differential equations on manifolds, existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications. Both the autonomous and nonautonomous case are considered. Moreover, a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on ce...

Meromorphic Solutions of First - Order Algebraic Differential Equations

i. P. Deligne, Usp. Mat. Nauk, 30, No. 5, 159-190 (1975). 2. H. Jacquet andR. P. Langlands, Automorphic Formson GL(2), Springer-Verlag (1970). 3. S. Banach,.Oeuvres, Vol. i, Warsawa (1967), pp. 318-322. 4. G. A. Margulis, Monatsh. Mmth., 9__0, No. 3, 233-235 (1980), 5. D. Sullivan, Bull. Am. Math. Soc., ~, No. i, 121-123 (1981). 6. R. A. Rank_in, Proc. Cambridge Philos. Soc., 35, 351-372 (1939)...

Some properties of algebraic difference equations of first order

Geometric Integration of Ordinary Differential Equations on Manifolds

This article illustrates how classical integration methods for differential equations on manifolds can be modified in order to preserve certain geometric properties of the exact flow. Projection methods as well as integrators based on local coordinates are considered. The central ideas of this article have been presented at the 40th anniversary meeting of the journal BIT. AMS subject classifica...

Finite Difference Approximations for Nonlinear First Order Partial Differential Equations

Classical solutions of nonlinear partial differential equations are approximated in the paper by solutions of quasilinear systems of difference equations. Sufficient conditions for the convergence of the method are given. The proof of the stability of the difference problem is based on a comparison method. This new approach to the numerical solving of nonlinear equations is generated by a linea...