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Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems

  • Li Zou , Songxin Liang EMAIL logo , Yawei Li and David J. Jeffrey
Published/Copyright: December 10, 2016
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 72 Issue 3

Abstract

Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

Keywords: Adomian Decomposition Method (ADM); Analytic Approximation; Homotopy Analysis Method (HAM); Nonlinear Boundary Value Problem

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 51379033

Award Identifier / Grant number: 51522902

Funding statement: The research was partially supported by the National Natural Science Foundation of China (51379033, 51522902).

Acknowledgments

The research was partially supported by the National Natural Science Foundation of China (51379033, 51522902).

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Received: 2016-9-30
Accepted: 2016-11-3
Published Online: 2016-12-10
Published in Print: 2017-3-1

©2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Hydrogen and Carbon Vapour Pressure Isotope Effects in Liquid Fluoroform Studied by Density Functional Theory
  3. Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems
  4. Resistance Distances and Kirchhoff Index in Generalised Join Graphs
  5. Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
  6. Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
  7. Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies
  8. Peristaltic Flow of Rabinowitsch Fluid in a Curved Channel: Mathematical Analysis Revisited
  9. Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium
  10. Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation
  11. Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations
  12. Discrete and Semidiscrete Models for AKNS Equation
https://doi.org/10.1515/zna-2016-0420
Keywords for this article
Adomian Decomposition Method (ADM); Analytic Approximation; Homotopy Analysis Method (HAM); Nonlinear Boundary Value Problem

Articles in the same Issue

  1. Frontmatter
  2. Hydrogen and Carbon Vapour Pressure Isotope Effects in Liquid Fluoroform Studied by Density Functional Theory
  3. Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems
  4. Resistance Distances and Kirchhoff Index in Generalised Join Graphs
  5. Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
  6. Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
  7. Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies
  8. Peristaltic Flow of Rabinowitsch Fluid in a Curved Channel: Mathematical Analysis Revisited
  9. Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium
  10. Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation
  11. Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations
  12. Discrete and Semidiscrete Models for AKNS Equation
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