scholarly journals Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Xiuming Li ◽  
Suping Qian
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Iteration Method ◽  
Source Term ◽  
Convergent Sequence ◽  
Variational Iteration Method ◽  
Equivalent Problem ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Reduced Problem

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method

2018 ◽  
Vol 13 (02) ◽  
pp. 2050042
Author(s):  
Fernane Khaireddine
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
General Formula ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Linear And Nonlinear

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

scholarly journals Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yongxiang Zhao ◽  
Aiguo Xiao ◽  
Li Li ◽  
Chengjian Zhang
Keyword(s):  
Singular Perturbation ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Variational Iteration Method ◽  
Variational Theory ◽  
Initial Value ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Convergence Results

The variational iteration method (VIM) is applied to solve singular perturbation initial value problems with delays (SPIVPDs). Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.

scholarly journals An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Sevimlican
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

He's variational iteration method (VIM) is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.

The Variational Iteration Method for an Inverse Problem of Finding a Source Parameter

2017 ◽  
Vol 9 (4) ◽  
pp. 861-867 ◽  
Author(s):  
Zongli Ma ◽  
Shumin Li
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Inverse Problems ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Source Parameter ◽  
Numerical Example ◽  
Variational Iteration ◽  
Unknown Source

AbstractAn inverse problem of determining unknown source parameter in a parabolic equation is considered. The variational iteration method (VIM) is presented to solve inverse problems. The solution gives good approximations by VIM. A numerical example shows that the VIM works effectively for an inverse problem.

scholarly journals Fractional variational iteration method for solving time-fractional Newell-Whitehead-Segel equation

2019 ◽  
Vol 8 (1) ◽  
pp. 164-171 ◽  
Author(s):  
Amit Prakash ◽  
Manish Goyal ◽  
Shivangi Gupta
Keyword(s):  
Numerical Method ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Variational Iteration

AbstractIn this paper, Newell–Whitehead–Segel equations of fractional order are solved by fractional variational iteration method. Convergence analysis and numerical examples are presented to show the efficiency of the proposed numerical method. Plotted graph demonstrate the mightiness and accurateness of the proposed technique.

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