a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or...

paper Manifolds Of Functions Defined By Systems Of Algebraic Differential Equations and 2 books, Differential Equations From The Algebraic Standpoint and...

In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several...

Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, ISBN 978-1-61197-139-2 Coddington, Earl A.; Levinson, Norman (1955). Theory of Ordinary...

partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients...

pseudo-differential equations use pseudo-differential operators instead of differential operators. A differential algebraic equation (DAE) is a differential...

two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true...

equations, System of bilinear equations, System of polynomial equations, System of differential equations, or a System of difference equations Simultaneous...

numerical integration of ordinary differential equations (ODEs) and differential algebraic equations (DAEs), to be used. A large number of integration routines...

optimization solution of linear and some non-linear equations over various domains solution of some differential and difference equations taking some limits...

simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree...

for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their...

these equations because of their relation to the Riccati differential equation. Indeed, the CARE is verified by the time invariant solutions of the associated...

certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure...

smoothness of solutions to the Navier–Stokes equations, named as one of the Millennium Prize Problems in 2000. Partial differential equations are ubiquitous...

Stochastic differential equations can also be extended to differential manifolds. Stochastic differential equations originated in the theory of Brownian...

operations Differential algebra – Algebraic study of differential equations Differential Galois theory – Study of Galois symmetry groups of differential fields...

mathematics, differential Galois theory is the field that studies extensions of differential fields. Whereas algebraic Galois theory studies extensions of algebraic...

differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations...

invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) the explicit determination of solutions in an explicit...

neurons can be described by a system of integro-differential equations, see for example the Wilson-Cowan model. The Whitham equation is used to model nonlinear...

Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis...

the study of differential equations for connections on bundles, and the resulting geometric moduli spaces of solutions to these equations as well as...

In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend...

theorem (algebraic topology) Homotopy excision theorem (algebraic topology) Hopf theorem (differential topology) Hurewicz theorem (algebraic topology)...

integration of ordinary differential equations (ODEs) and differential-algebraic systems of equations (DAEs). Many integration routines have been developed...

theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter...

of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows...