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Displaying 21 – 38 of 38

On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar, Enrique A. Navarro (1989)

Aplikace matematiky

In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...

On the numerical solution of implicit two-point boundary-value problems

Jaroslav Doležal, Jiří Fidler (1979)

Kybernetika

On the Numerical Treatment of a Small Divisor Problem.

E. Zehnder, D. Braess (1982)

Numerische Mathematik

On the Optimum Choice of Weight Functions in a Class of Variational Calculations.

L.M. Delves, M. Bain (1976/1977)

Numerische Mathematik

On the Reduction of Holt's Problem to a Finite Interval.

Katalin, Vicsek, Mária Balla (1987)

Numerische Mathematik

On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.

Goebbels, St.J. (1999)

Journal of Inequalities and Applications [electronic only]

On the stability of solutions of a multipoint boundary value problem for a system of generalized ordinary differential equations.

Ashordia, Malkhaz (1995)

Memoirs on Differential Equations and Mathematical Physics

On the Stability of the Ritz Procedure for Nonlinear Problems.

A.I. Schiop (1974/1975)

Numerische Mathematik

On the stability of the Ritz procedure for nonlinear two-point boundary value problems

Schiop, Alexandru I. (1979)

Portugaliae mathematica

On the worst scenario method: Application to uncertain nonlinear differential equations with numerical examples

Harasim, Petr (2010)

Programs and Algorithms of Numerical Mathematics

One-step methods for ordinary differential equations with parameters

Tadeusz Jankowski (1990)

Aplikace matematiky

In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.

One-step methods for two-point boundary value problems in ordinary differential equations with parameters

Tadeusz Jankowski (1994)

Applications of Mathematics

A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets $h_{n}$ , one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively.

Opposing flows in a one dimensional convection-diffusion problem

Eugene O’Riordan (2012)

Open Mathematics

In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...

Optimal Convective Heat-Transport

Josef Dalík, Oto Přibyl (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The one-dimensional steady-state convection-diffusion problem for the unknown temperature $y (x)$ of a medium entering the interval $(a, b)$ with the temperature $y_{min}$ and flowing with a positive velocity $v (x)$ is studied. The medium is being heated with an intensity corresponding to $y_{max} - y (x)$ for a constant $y_{max} > y_{min}$ . We are looking for a velocity $v (x)$ with a given average such that the outflow temperature $y (b)$ is maximal and discuss the influence of the boundary condition at the point $b$ on the “maximizing” function $v (x)$ .

Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem

Roman Šimeček (2013)

Applications of Mathematics

A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...

Optimal discrete approximation of continuous linear operators applicable to control problems

Antonín Tuzar (1985)

Kybernetika

Optimal solution of some two-point boundary value problem

Boleslaw Z. Kacewicz (1990)

Banach Center Publications

Optimale Fehlerabschätzungen mit dualen Funktionalen bei semilineraen Randwertaufgaben gewöhnlicher Differentialgleichungen.

F. Geistbeck, A. Sachs (1974)

Numerische Mathematik

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