• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.465-472
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• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.813-831
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• 2000

In recent years, the theory of Wiener-Hopf equations has emerged as a novel and innovative technique for developing efficient and powerful numerical methods for solving variational inequalities and complementarity problems. In this paper, we provide an account of some of the fundamental aspects of the Wiener-Hopf equations with major emphasis on the formulation, computational algorithms, various generalizations and their applications. We also suggest some open problems for further research with sufficient information and references.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.569-572
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• 1999

This paper presents a method for designing an autopilot of the BTT missile using 2DOF Wiener-Hopf control technique to improve tracking performance. Linear controllers are designed based on the linearized models which are obtained from the nonlinear missile dynamic equations at various operating points. The gain scheduling technique is used to implement the final autopilot. A simulation on the flight of missiles is carried out through the use of 6DOF equation program including exact nonlinear equations of the missile and the variations of aerodynamic variables in order to check applicability of the suggested method in real situation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.243-291
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• 2020

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂ VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.659-668
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• 1998

In this paper we introduce and study a new class of gen-eralized mildly nonlinear complementarity problems for fuzzy map-pings. We use the change of variabes technique to establish the equivalence between the generalized mildly nonlinear complementar-ity problems and the Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithm for solv-ing the generalized mildly nonlinear complemetarity problems.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.6
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• pp.45-56
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• 1999

This paper presents a method for designing an autopilot of the BTT missile using 2DOF Wiener-Hopf control technique to improve tracking performance. Linear controllers are designed based on the linearized models which are obtained from the nonlinear missile dynamic equations at various operating points. The gain scheduling technique is used to implement the final autopilot. A simulation on the flight of missiles is carried out through the use of 6DOF equation program including exact nonlinear equations of the missile and the variations of aerodynamic variables in order to check applicability of the suggested method in real situation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.1016-1019
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• 2002

This paper deals with a fundamental and classical scattering problem by a finite strip. For the analysis of scattered acoustic field, a “single” integral equation is derived. Firstly, the complexity by considering the effect of the mean flow is alleviated by the introduction of Prandtl-Glauert coordinate and the new dependent variable. Secondly, the difficulty of solving the resultant strongly-coupled integral equations which always appear in this kind of 3-part mixed boundary value problem is solved by observing some good properties of the functions in complex domain and manipulating the equations and variables for the use of those properties. The solution can be obtained asymptotically in terms of gamma function and Whittaker function. One aim of this study is the improvement of methodology for the research using integral equations. The other is the basic understanding of scattering by a finite strip related to the linear cascade model of rotating fan blades.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.1
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• pp.43-53
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• 2008

Surface edge crack in transversely isotropic piezoelectric material is analyzed. The concentrated antiplane mechanical and inplane electrical loadings are applied to an arbitrary point of the surface, where the impermeable crack boundary condition is imposed. Using Mellin transform the problem is formulated, from which Wiener-Hopf equations are derived. By solving the equations the solution is obtained in a closed form. Mechanical and electric intensity factors and energy release rate are obtained and discussed. This problem could be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.73-90
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• 1998

In this paper we introduce and study a number of new classes of quasi variational inequalities. using essentially the projection technique and its variant forms we prove that the gen-eralized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations(normal maps). This equivalence enables us to suggest a number of iterative algorithms solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational in-equalities we obtain a class of quasi variational inequalities studied by Siddiqi Husain and Kazmi [35] but there are several inaccuracies in their formulation of the problem the statement and the proofs of the problem the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of thir results can be obtained as special cases from our main results.