Results 171 to 180 of about 17,997 (206)

Implicit elliptic differential equations

Set-Valued Analysis, 1994
The author studies the implicit differential equation \(f(x,u,Du,Lu) = 0\), where \(x \in \Omega \subset \mathbb{R}^ n\), \(u \in \mathbb{R}^ m\), \(Du = (Du_ 1, \dots, Du_ m)\), \(Lu = (Lu_ 1, \dots, Lu_ m)\), and \(f\): \(\Omega \times \mathbb{R}^ m \times \mathbb{R}^{mn} \times \mathbb{R}^ m \to \mathbb{R}\) is given.
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Envelope Solutions for Implicit Ordinary Differential Equations

IMA Journal of Numerical Analysis, 1990
Implicit ordinary differential equations \(f(x,y,y')=0\) are studied. A method for the computation of the envelope solutions is given which is similar to the predictor-corrector method. Some numerical examples are given, error estimations are not studied.
Gilbert, J., Light, W. A.
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Implicit schemes for differential equations

Journal of Computational Physics, 1982
Abstract Implicit high-order accurate temporal-integration schemes are developed to reduce partial differential equations of evolution type to a sequence of ordinary differential equations involving the spatial directions only. The ordinary differential equations are solved using various accurate integration methods.
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Implicit methods for implicit differential equations

1969
Quadrature methods are used to obtain numerical solutions of certain systems of implicit differential equations. Several examples indicate the range of application of the methods.
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Explicit Ordinary Differential Equations

1998
In the last chapter we discussed the numerical treatment of explicit ordinary differential equations. Here, we will consider the more general case, implicit ordinary differential equations.
Edda Eich-Soellner, Claus Führer
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Singularities of implicit ordinary differential equations

ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187), 2002
This paper concerns quasi-linear implicit differential equations of form 0=A/sub 1/(x)x/spl dot/-g/sub 1/(x), 0=g/sub 2/(x), where A/sub 1/: U/spl rarr/L(R/sup n/,R/sup n-m/)/spl isin/C/sup 1/, g/sub l/: U/spl rarr/R/sup n-m//spl isin/C/sup 1/, g/sub 2/: U/spl rarr/R/sup m//spl isin/C/sup 2/, U/spl sube/R/sup n/ is open, n, m/spl isin/N, and ...
G. Reissig, H. Boche
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Existence for an implicit nonlinear differential equation

Nonlinear Analysis: Theory, Methods & Applications, 1998
The authors prove some existence results concerning the implicit Cauchy problem in the triplet \(V\subset H\subset V'\) of real Hilbert spaces: \[ (Bu)'(t)+ Au(t)\ni f(t),\quad Bu(0)= u_0, \] where \(B\in L(V, V')\) is symmetric and nonnegative and \(A: V\to V'\) is nonlinear, maximal monotone with \(\lambda_0 B+A\) coercive for some \(\lambda_0\geq 0\)
Barbu, Viorel, Favini, Abgelo
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Implicit differential equations of gas dynamics

Journal of Mathematical Sciences, 2012
We describe three remarkable examples of partially invariant solutions to equations of gas dynamics. Two examples are connected with invariant submodels of the stationary and projective Ovsyannikov vortex. Bibliography: 15 titles. Illustrations: 5 figures.
A. A. Cherevko, A. P. Chupakhin
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On the Solvability of Implicit Functional Equations with Applications to Discontinuous Differential Equations

Acta Mathematica Sinica, English Series, 2005
The author proves some existence results for the functional equations \(v(t)=F(t,\varphi(v), v)\) and \(v(t)=f(t,\varphi(v)(t), v(t))\) for almost every \(t\in J\) in the space \(L^p(J,E) \quad (1 \leq p < \infty)\), where \(E\) is an ordered Banach space, \(J\) is a compact real interval, \(F: J \times L^p(J,E) \times L^p(J,E) \to E\), \(f: J \times E
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Singularities of Implicit Differential Equations and Static Bifurcations

2013
We discuss geometric singularities of implicit ordinary differential equations from the point of view of Vessiot theory. We show that quasi-linear systems admit a special treatment leading to phenomena not present in the general case. These results are then applied to study static bifurcations of parametric ordinary differential equations.
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