Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
Numerical Solutions to the Darboux Problem with the Functional Dependence
-
Z. Kamont
Veröffentlicht/Copyright:
23. Februar 2010
Abstract
The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(x, y)) where z(x, y) is a function defined by z(x, y)(t, s) = z(x + t, y+ s), (t, s) ∈ [–a0, 0] × [–b0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means of a comparison method; moreover we give an error estimate. The convergence of explicit difference schemes is proved under a general assumption that given functions satisfy nonlinear estimates of the Perron type. Our results are illustrated by a numerical example.
Key words and phrases.: Volterra condition; differential-integral equation; implicit functional-difference equation; comparison method; nonlinear estimate
Received: 1995-12-18
Published Online: 2010-02-23
Published in Print: 1998-February
© 1998 Plenum Publishing Corporation
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
Schlagwörter für diesen Artikel
Volterra condition;
differential-integral equation;
implicit functional-difference equation;
comparison method;
nonlinear estimate
Artikel in diesem Heft
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
