scholarly journals Variational Problems with Moving Boundaries Using Decomposition Method

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Reza Memarbashi
Keyword(s):  
Boundary Conditions ◽  
Decomposition Method ◽  
Lagrange Equation ◽  
Adomian Decomposition Method ◽  
Variational Problems ◽  
Moving Boundaries ◽  
Natural Boundary ◽  
Transversality Conditions ◽  
Adomian Decomposition ◽  
Natural Boundary Conditions

The aim of this paper is to present a numerical method for solving variational problems with moving boundaries. We apply Adomian decomposition method on the Euler-Lagrange equation with boundary conditions that yield from transversality conditions and natural boundary conditions.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

Closed-form solution for a rectangular stepped fin involving all variable thermal parameters and nonlinear boundary conditions

2016 ◽  
Vol 231 (5) ◽  
pp. 992-1010 ◽  
Author(s):  
Kuljeet Singh ◽  
Ranjan Das ◽  
Rohit K Singla
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Conditions ◽  
Thermal Parameters ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Adomian Decomposition

In this paper, the implementation of the Adomian decomposition method is demonstrated to solve a nonlinear heat transfer problem for a stepped fin involving all temperature-dependent means of heat transfer and nonlinear boundary conditions. Unlike conventional insulated tip assumption, to make the present problem more practical, the fin tip is assumed to disperse heat by convection and radiation. Thermal parameters such as the thermal conductivity, the surface heat transfer coefficient and the surface emissivity are considered to be temperature-dependent. Adomian polynomials are first obtained and then a set of Adomian decomposition method results is validated with pertinent results of the differential transformation method reported in the literature. Effects of different thermo-physical parameters on the temperature distribution and the efficiency have been exemplified. The study reveals that for a given set of conditions, the stepped fin may perform better than the straight fin.

scholarly journals Natural Boundary Conditions in Geometric Calculus of Variations

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Giovanni Moreno ◽  
Monika Ewa Stypa
Keyword(s):  
Boundary Conditions ◽  
Variational Problems ◽  
Boundary Values ◽  
Natural Boundary ◽  
Natural Behavior ◽  
Geometric Calculus ◽  
Jet Bundles ◽  
Independent Variables ◽  
Natural Boundary Conditions ◽  
Dimensional Domain

AbstractIn this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of Y - the manifold of dependent and independent variables underlying a given problem - as well as the order of its Lagrangian. Our result follows from the natural behavior, under boundary-friendly transformations, of an operator, similar to the Euler map, constructed in the context of relative horizontal forms on jet bundles (or Grassmann fibrations) over Y . Explicit examples of natural boundary conditions are obtained when Y is an (n + 1)-dimensional domain in ℝ

scholarly journals The use of Adomian decomposition method for solving problems in calculus of variations

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mehdi Tatari
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Variational Problem ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Problems ◽  
Convergent Power Series ◽  
Adomian Decomposition

In this paper, a numerical method is presented for finding the solution of some variational problems. The main objective is to find the solution of an ordinary differential equation which arises from the variational problem. This work is done using Adomian decomposition method which is a powerful tool for solving large amount of problems. In this approach, the solution is found in the form of a convergent power series with easily computed components. To show the efficiency of the method, numerical results are presented.

Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method

2017 ◽  
Vol 23 (9) ◽  
pp. 1345-1363 ◽  
Author(s):  
Desmond Adair ◽  
Martin Jaeger
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Free Vibration Analysis ◽  
Published Data ◽  
Bernoulli Beam ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

The governing equations for a pre-twisted rotating cantilever beam are derived and used for free vibration analysis of a pre-twisted rotating beam whose flexural displacements are coupled in two planes. First differential equations of motion of a rotating twisted beam, including terms due to centrifugal stiffening, are derived for an Euler–Bernoulli beam undergoing free natural vibrations. The general solutions of these equations are obtained on applying the Adomian modified decomposition method (AMDM). The AMDM allows the governing differential equations to become recursive algebraic equations and the boundary conditions to become simple algebraic frequency equations suitable for symbolic computation. With additional simple mathematical operations on the model, the natural frequencies and corresponding closed-form series solution of the mode shape can be obtained simultaneously. Two main advantages of the application of the AMDM are, for the cases considered here, its fast convergence rate to the solution with the high degree of accuracy. As the AMDM technique is systematic, it is found straight-forward to modify boundary conditions from one case to the next. Comparison of results with published data showed the present calculations to be in reasonable agreement.

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