Erno Scheiber - Academia.edu (original) (raw)

Papers by Erno Scheiber

Research paper thumbnail of Adjoint System in the Shooting Method to Solve Boundary Value Problems

arXiv (Cornell University), Sep 28, 2022

Research paper thumbnail of On the maximization of some nonlinear functionals using a Jensen type inequality

(1) Demonstratio Mathematica, 37(2004), no.3, 719-726. (2) 16th Scientific Session on Mathematics and its Applications. Braşov, 2002, 109-115. , 2004

Models of fluid mechanics phenomena like the deflector of maximal drag or maximal lifting lead to... more Models of fluid mechanics phenomena like the deflector of maximal drag or maximal lifting lead to maximization problems whose solutions are ob-tained using a method based on a Jensen inequality. The purpose of this paper is to point out the united character of the given solutions. A scheme is derived for an unconstrained and for a constrained maximization problem, which is applied to four examples.

Research paper thumbnail of On the convergence of the variational iteration method

Convergence results are stated for the variational iteration method applied to solve an initial v... more Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

Research paper thumbnail of Adjoint system in the shooting method to solve boundary value problems

Bulletin of the "Transilvania" University of Braşov, Dec 29, 2022

The shooting method is used to solve a boundary value problem with separated and explicit constra... more The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to the given differential system. Finally the Newton-Kantorovich iterations are regained.

Research paper thumbnail of On the Variational Iteration Method for the Nonlinear Volterra Integral Equation

arXiv (Cornell University), Jul 16, 2019

The variational iteration method is used to solve nonlinear Volterra integral equations. Two appr... more The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.

Research paper thumbnail of Java in Scientific Computation An educational approach

The aim of this paper is to emphasize some specific aspects when numerical methods are implemente... more The aim of this paper is to emphasize some specific aspects when numerical methods are implemented in Java like involved programming problems, available resources and the possibility to extend the application usage in a distribute environment, like Internet.

Research paper thumbnail of A Hahn-Banach type extension theorem for linear mapping into ordered modules

Research paper thumbnail of Monotonic linear extension for ordered modules their extremality and uniqueness

Research paper thumbnail of An adaptive precision algorithm for numerical solution of optimal control problems by sucessive approximation metod

Research paper thumbnail of Chernousko-Lyubushin Version of the Successive Approximation Method for Optimal Control Problem Revisited

Bulletin of the Transilvania University of Brasov

The purpose of this paper is to emphesize the parallel property of a variant of the successive ap... more The purpose of this paper is to emphesize the parallel property of a variant of the successive approximation method to solve the optimal control problem for ordinary di�fferential equations. The obtained parallel algorithm combines synchronous and asynchronous computations.

Research paper thumbnail of Numerical solutions of an implicit differential equation for some inverse problems of mechanism theory

Research paper thumbnail of A Tspaces Based Framework for Parallel-Distributed Applications

A framework enabling the deployment and the execution of a parallel-distribute application is pre... more A framework enabling the deployment and the execution of a parallel-distribute application is presented. The application is build on an imposed template based on the master-slave model. The application as well as the infrastructure of the framework use TSpaces servers. The coordination of the activities of the application is of data driven type.

Research paper thumbnail of On the parallel version of the successive approximation method for quasilinear boundary value problem

Journal of Computational and Applied Mathematics, 1996

The convergence properties of the successive approximation method to solve a quasilinear two poin... more The convergence properties of the successive approximation method to solve a quasilinear two points boundary value problem is studied. The successive approximation method is used to solve the parallel/multiple version of the problem. Conditions which assure the convergence of the method and error bound are given.

Research paper thumbnail of A Parallel Version of a Multistep Method to Solve the Initial Value Problem

Research paper thumbnail of Logarithmic growth in biological processes

UKSim2010 - UKSim 12th International Conference on Computer Modelling and Simulation, 2010

The aim of our paper is to approximate the parameters of a generic logarithmic function that can ... more The aim of our paper is to approximate the parameters of a generic logarithmic function that can be used to model various biological processes. We are considering the Gauss-Newton algorithm for solving the non-linear least squares problem and we are proposing a method for selecting the initial choice for the algorithm. This method proves to considerably increase the convergence probability

Research paper thumbnail of On the Gradient Method Applied to Optimal Control Problem

Bulletin of the Transilvania University of Braşov,, 2014

The purpose of this paper is to give direct proofs of some convergence results for the gradient a... more The purpose of this paper is to give direct proofs of some convergence results for the gradient and gradient projection methods applied to optimal control problem. The methods are considered in the continuous approach. In the context of optimal control problem, direct proofs are given to the results from the point of view of the teaching methods. The gradient projection method is studied in a modi�ed variant, which is programmed in a simpler way in a Computer Algebra System (CAS) environment. For simple optimal control problems it is possible to use symbolic computations. An example is solved in Mathematica CAS.

Research paper thumbnail of On the convergence of a method for solving two point boundary value problems by optimal control

Using the idea of the least squares method, a nonlinear two point boundary value problem is trans... more Using the idea of the least squares method, a nonlinear two point boundary value problem is transformed into an optimal control problem. For solving the optimal control problem the gradient method is used. The convergence of the method is investigated and numerical results are reported.

Research paper thumbnail of On representation of a first degree spline function

SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 2021

A presentation of related global representations for the first degree spline function is given, r... more A presentation of related global representations for the first degree spline function is given, revisiting some known results. The given global representations are deduced one from another by simple transformations.

Research paper thumbnail of The numerical solution of Theodorsen integral equation

Computers & Mathematics with Applications, 1999

In this paper, a numerical solution of the Theodorsen integral equation is studied. Using an adeq... more In this paper, a numerical solution of the Theodorsen integral equation is studied. Using an adequate quadrature formula which eliminates the singularity of the integral part of the Theodorsen equation, we obtain a system of nonlinear algebralcal equations. This system may be solved using a Jacobi type method and the procedure can be easily implemented using a programming language with parallel facilities. Examples are given using ADA, EVAL, and PARALLAXIS. A convergence result is established. (~

Research paper thumbnail of A Direct Approach for Time Optimal Control Problem with Linear Differential System

The purpose of this paper is to present an approach to solve the time-optimal control problem. Wh... more The purpose of this paper is to present an approach to solve the time-optimal control problem. While searching the control as a piecewise constant function the optimal control problem is reduced to a nonlinear programming problem. Two examples are presented, in which cases the computation is carried out with the Mathematica software.

Research paper thumbnail of Adjoint System in the Shooting Method to Solve Boundary Value Problems

arXiv (Cornell University), Sep 28, 2022

Research paper thumbnail of On the maximization of some nonlinear functionals using a Jensen type inequality

(1) Demonstratio Mathematica, 37(2004), no.3, 719-726. (2) 16th Scientific Session on Mathematics and its Applications. Braşov, 2002, 109-115. , 2004

Models of fluid mechanics phenomena like the deflector of maximal drag or maximal lifting lead to... more Models of fluid mechanics phenomena like the deflector of maximal drag or maximal lifting lead to maximization problems whose solutions are ob-tained using a method based on a Jensen inequality. The purpose of this paper is to point out the united character of the given solutions. A scheme is derived for an unconstrained and for a constrained maximization problem, which is applied to four examples.

Research paper thumbnail of On the convergence of the variational iteration method

Convergence results are stated for the variational iteration method applied to solve an initial v... more Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

Research paper thumbnail of Adjoint system in the shooting method to solve boundary value problems

Bulletin of the "Transilvania" University of Braşov, Dec 29, 2022

The shooting method is used to solve a boundary value problem with separated and explicit constra... more The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to the given differential system. Finally the Newton-Kantorovich iterations are regained.

Research paper thumbnail of On the Variational Iteration Method for the Nonlinear Volterra Integral Equation

arXiv (Cornell University), Jul 16, 2019

The variational iteration method is used to solve nonlinear Volterra integral equations. Two appr... more The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.

Research paper thumbnail of Java in Scientific Computation An educational approach

The aim of this paper is to emphasize some specific aspects when numerical methods are implemente... more The aim of this paper is to emphasize some specific aspects when numerical methods are implemented in Java like involved programming problems, available resources and the possibility to extend the application usage in a distribute environment, like Internet.

Research paper thumbnail of A Hahn-Banach type extension theorem for linear mapping into ordered modules

Research paper thumbnail of Monotonic linear extension for ordered modules their extremality and uniqueness

Research paper thumbnail of An adaptive precision algorithm for numerical solution of optimal control problems by sucessive approximation metod

Research paper thumbnail of Chernousko-Lyubushin Version of the Successive Approximation Method for Optimal Control Problem Revisited

Bulletin of the Transilvania University of Brasov

The purpose of this paper is to emphesize the parallel property of a variant of the successive ap... more The purpose of this paper is to emphesize the parallel property of a variant of the successive approximation method to solve the optimal control problem for ordinary di�fferential equations. The obtained parallel algorithm combines synchronous and asynchronous computations.

Research paper thumbnail of Numerical solutions of an implicit differential equation for some inverse problems of mechanism theory

Research paper thumbnail of A Tspaces Based Framework for Parallel-Distributed Applications

A framework enabling the deployment and the execution of a parallel-distribute application is pre... more A framework enabling the deployment and the execution of a parallel-distribute application is presented. The application is build on an imposed template based on the master-slave model. The application as well as the infrastructure of the framework use TSpaces servers. The coordination of the activities of the application is of data driven type.

Research paper thumbnail of On the parallel version of the successive approximation method for quasilinear boundary value problem

Journal of Computational and Applied Mathematics, 1996

The convergence properties of the successive approximation method to solve a quasilinear two poin... more The convergence properties of the successive approximation method to solve a quasilinear two points boundary value problem is studied. The successive approximation method is used to solve the parallel/multiple version of the problem. Conditions which assure the convergence of the method and error bound are given.

Research paper thumbnail of A Parallel Version of a Multistep Method to Solve the Initial Value Problem

Research paper thumbnail of Logarithmic growth in biological processes

UKSim2010 - UKSim 12th International Conference on Computer Modelling and Simulation, 2010

The aim of our paper is to approximate the parameters of a generic logarithmic function that can ... more The aim of our paper is to approximate the parameters of a generic logarithmic function that can be used to model various biological processes. We are considering the Gauss-Newton algorithm for solving the non-linear least squares problem and we are proposing a method for selecting the initial choice for the algorithm. This method proves to considerably increase the convergence probability

Research paper thumbnail of On the Gradient Method Applied to Optimal Control Problem

Bulletin of the Transilvania University of Braşov,, 2014

The purpose of this paper is to give direct proofs of some convergence results for the gradient a... more The purpose of this paper is to give direct proofs of some convergence results for the gradient and gradient projection methods applied to optimal control problem. The methods are considered in the continuous approach. In the context of optimal control problem, direct proofs are given to the results from the point of view of the teaching methods. The gradient projection method is studied in a modi�ed variant, which is programmed in a simpler way in a Computer Algebra System (CAS) environment. For simple optimal control problems it is possible to use symbolic computations. An example is solved in Mathematica CAS.

Research paper thumbnail of On the convergence of a method for solving two point boundary value problems by optimal control

Using the idea of the least squares method, a nonlinear two point boundary value problem is trans... more Using the idea of the least squares method, a nonlinear two point boundary value problem is transformed into an optimal control problem. For solving the optimal control problem the gradient method is used. The convergence of the method is investigated and numerical results are reported.

Research paper thumbnail of On representation of a first degree spline function

SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 2021

A presentation of related global representations for the first degree spline function is given, r... more A presentation of related global representations for the first degree spline function is given, revisiting some known results. The given global representations are deduced one from another by simple transformations.

Research paper thumbnail of The numerical solution of Theodorsen integral equation

Computers & Mathematics with Applications, 1999

In this paper, a numerical solution of the Theodorsen integral equation is studied. Using an adeq... more In this paper, a numerical solution of the Theodorsen integral equation is studied. Using an adequate quadrature formula which eliminates the singularity of the integral part of the Theodorsen equation, we obtain a system of nonlinear algebralcal equations. This system may be solved using a Jacobi type method and the procedure can be easily implemented using a programming language with parallel facilities. Examples are given using ADA, EVAL, and PARALLAXIS. A convergence result is established. (~

Research paper thumbnail of A Direct Approach for Time Optimal Control Problem with Linear Differential System

The purpose of this paper is to present an approach to solve the time-optimal control problem. Wh... more The purpose of this paper is to present an approach to solve the time-optimal control problem. While searching the control as a piecewise constant function the optimal control problem is reduced to a nonlinear programming problem. Two examples are presented, in which cases the computation is carried out with the Mathematica software.