• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• 충청수학회지
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• 제25권4호
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• pp.669-676
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• 2012

In this note we extend one well-known iteration formula to derive new third-order methods for solving a nonlinear equation. The comparison with other methods is given.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.335-341
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• 2009

In this paper, a system of nonsmooth equations reformulated from a nonlinear complementarity problem with nonsmooth data is studied. The formulas of some subdifferentials for related functions in this system of nonsmooth equations are developed. The present work can be applied to Newton methods for solving this kind of nonlinear complementarity problem.

• 천문학논총
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• 제7권1호
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• pp.107-148
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• 1992

This paper presents a cosmological perturbation analysis in a Newtonian framework, using the Newtonian multi component version of the relativistic covariant equations. This work considers the fully nonlinear evolution of the perturbations, and is generalized to multicomponent systems and imperfect fluids. Known nonlinear solutions are presented in a general framework. Quasi-nonlinear analysis, considering both the compressible and rotational modes, is presented, including cases already known in the literature. The Fourier space representation of the conservation equations is also derived in a general context, with various decompositions of the velocity field. Commonly accepted cosmogonical frameworks are critically examined in the context of nonlinear evolution. This work may be regarded as the Newtonian counterpart of a recently presented general relativistic covariant formulation.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.1378-1383
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• 2003

A ferroelectric (called piezoelectric afterwards) wafer has been widely used as a key component of actuators or sensors of a layer type. According to recent researches, the piezoelectric wafer behaves in a nonlinear way under excessive electro-mechanical loadings. In the present paper, one-dimensional constitutive equations for the nonlinear behavior of a piezoelectric wafer are proposed based on the principles of thermodynamics and a simple viscoplasticity theory. The predictions of the developed model are compared with experimental observations.

• Earthquakes and Structures
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• 제13권2호
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• pp.131-136
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• 2017

This paper concerns two new analytical approaches for solving high nonlinear vibration equations. Energy Balance method and Hamiltonian Approach are presented and successfully applied for nonlinear vibration equations. In these approaches, there is no need to use small parameters to solve and only with one iteration, high accurate results are reached. Numerical procedures are also presented to compare the results of analytical and numerical ones. It has been established that, the proposed approaches are in good agreement with numerical solutions.

• Advances in nano research
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• 제15권2호
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Steel and Composite Structures
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• 제25권4호
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• pp.497-503
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• 2017

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.