• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.539-552
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• 2000

In this paper, we established the general comparison principles for IVP of impulsive differential equations with time variables, which strictly extend and improve the precious comparison results obtained by V. Lakes. et.al . and S.K.Kaul([3]-[7]). Whit the general comparison results, we constructed the monotone iterative sequences of solution for IVP of such equations which converges the maximal and minimal and minimal solutions , respectively.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.899-909
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• 1992

An iterative solution technique is presented to analyze the dynamic systems of rigid bodies subjected to kinematic constraints. Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Constraints on the velocity and acceleration as well as the position are made to be satisfied at joints at each time step. Time integration is efficiently performed because decomposition or orthonormalization of the large matrix is not required at all. An acceleration technique is suggested for the faster convergence of the iterative scheme.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.205-235
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• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.391-399
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• 2004

In this paper, we develop an iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities in Hilbert spaces. The resolvent operator technique is used to establish the equivalence between variational inequalities and fixed point problems. This equivalence is used to study the existence of a solution of nonlinear mixed implicit variational inequalities and to suggest an iterative algorithm for solving variational inequalities. In our results, we do not assume that the mapping is strongly monotone.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1651-1656
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• 1995

The adhesively bonded tubular single lap joint shows large nonlinear behavior in the loaddisplacement relation, because structural adhesives for the joint are usually rubber toughened, which endows adhesives with nonlinear shear properties. since the majority of load transfer of the adhesively bonded tubular single lap joint is accomplished by the nonlinear behavior of the adhesive, its torque transmission capability should be calculated incorporating nonlinear shear properties. However, both the analytic and numerical analyses become complicated if the nonlinear shear properties of the adhesive are included during the calculation of torque transmission capabilities. In this paper, in order to obtain the torque transmission capabilities easily, an iterative solution which includes the nonlinear shear properties of the adhesive was derived using the analytic solution with the linear shear properties of the adhesive. Since the iterative solution can be obtained very fast due to its simplicity, it has been found that it can be used in the design of the adhesively bonded tubular single lap joint.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Honam Mathematical Journal
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• v.15 no.1
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• pp.105-120
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• 1993

The auxiliary principle technique is used to prove the uniqueness and the existence of solutions for a class of nonlinear variational inequalities and suggest an innovative iterative algorithm for computing the approximate solution of variational inequalities. Error estimates for the finite element approximation of the solution of variational inequalities are derived, which refine the previous known results. An example is given to illustrate the applications of the results obtained. Several special cases are considered and studied.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.1
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• pp.14-30
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• 1985

Recently, multiple criteria decision making has been well established as a practical approach to seek a satisfactory solution to a decision making problem. Goal programming is one of the most powerful MCDM tools with satisfying operational assumptions that reflect the actual decision making process in real-world situations. In this paper we propose an efficient method implemented on a microcomputer for solving linear goal programming problems. It is an iterative revised goal simplex method using the sparsity technique. We design as interactive software package for microcomputers based on this method. From some computational experiences, we can state that the revised iterative goal simplex method using the sparsity technique is the most efficient one for microcomputer for solving goal programming problems.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.211-230
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• 2008

Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration presented here appears to be more efficient, while the Lanczos approach has roughly equal efficiency. The methods proposed are robust and efficient. Large size tests show that the improvement in terms of CPU time and storage is tremendous. Also reported is an aggressive shifting technique for the subspace iteration method, based on the mode error convergence criteria. A backward technique is introduced when the shift is not located in the right region. The efficiency of such a technique was demonstrated in the numerical tests.