Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems

2013 ◽  
Vol 49 ◽  
pp. 159-169 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Randolph Rach ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Electrostatic Actuators ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Beam Type

scholarly journals Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method

2020 ◽  
pp. 49-60
Author(s):  
Justina Mulenga ◽  
Patrick Azere Phiri
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.

A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Jun-Sheng Duan ◽  
Randolph Rach ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Matching Equation

AbstractIn this paper, we present a reliable algorithm to calculate positive solutions of homogeneous nonlinear boundary value problems (BVPs). The algorithm converts the nonlinear BVP to an equivalent nonlinear Fredholm– Volterra integral equation.We employ the multistage Adomian decomposition method for BVPs on two or more subintervals of the domain of validity, and then solve the matching equation for the flux at the interior point, or interior points, to determine the solution. Several numerical examples are used to highlight the effectiveness of the proposed scheme to interpolate the interior values of the solution between boundary points. Furthermore we demonstrate two novel techniques to accelerate the rate of convergence of our decomposition series solutions by increasing the number of subintervals and adjusting the lengths of subintervals in the multistage Adomian decomposition method for BVPs.

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

2017 ◽  
Vol 72 (3) ◽  
pp. 201-206
Author(s):  
Li Zou ◽  
Songxin Liang ◽  
Yawei Li ◽  
David J. Jeffrey
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Parameter Method ◽  
Nonlinear Boundary Value Problems ◽  
Electromechanical Systems ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Beam Type ◽  
Two Parameter

AbstractNonlinear 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.

scholarly journals A Modified Adomian Decomposition Method for Solving Higher-Order Singular Boundary Value Problems

2010 ◽  
Vol 65 (12) ◽  
pp. 1093-1100 ◽  
Author(s):  
Weonbae Kim ◽  
Changbum Chun
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Adomian Polynomials ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, we present a reliable modification of the Adomian decomposition method for solving higher-order singular boundary value problems. He’s polynomials are also used to overcome the complex and difficult calculation of Adomian polynomials occurring in the application of the Adomian decomposition method. Numerical examples are given to illustrate the accuracy and efficiency of the presented method, revealing its reliability and applicability in handling the problems with singular nature.

scholarly journals Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hossein Jafari ◽  
Khadijeh Bagherian ◽  
Seithuti P. Moshokoa
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Type Problem ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. We solve the fractional Bratu-type problem as an illustrative example.

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