Nonlinear two-point boundary value problems

In this paper we present, in a framework of 1D-membrane Micro-Electro-MechanicalSystems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steadystate case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychonoff's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.

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“…It is well-know [31] that (23), by differentiation, can be transformed in the following integral equation:…”

Section: A Results Of Existence For P Roblem Imentioning

confidence: 99%

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Barba

Fattorusso

Versaci

2017

Communications in Applied and Industrial Mathematics

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“…y y x . For obtaining an approximate value y , of the theoretical solution y x of the problem (1), that purpose, following the ideas in [9,10], we propose multistep difference method as,…”

Section: Derivation and Development Of The Methodsmentioning

confidence: 99%

“…The specific assumption on f x, y , to ensure existence and uniqueness will not be considered [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…A sixth order three point discretization for problem (1) is given by Chawla [5]. These methods based on the polynomial functions, which are normally smooth and sufficient continuous derivatives.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, we describe a sixth order finite difference method for differential equation (1). The method is based on rational function approximation and its development based on power series expansions (Taylor and binomial).…”

Section: Introductionmentioning

confidence: 99%

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A Finite Difference Method of High Order Accuracy for the Solution of Two-Point Boundary Value Problems

Pandey

2014

Acta Tech Jaur

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We present a new high order finite difference method for second order differential equation y x f x, y subject to boundary conditions y a α and y b β . The method is based on rational function approximation and its development is based on power series expansions. Under appropriate conditions, local truncation error calculated and order of method estimated six. Our finite difference method leads to nonlinear system of equations. Numerical examples are given to illustrate the effectiveness, efficiency and high order accuracy of the method.

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