## He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation.(English)Zbl 1131.65084

Summary: The well known variational iteration method is used for finding the solution of a semi-linear inverse parabolic equation. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method a rapid convergent sequence is produced which tends to the exact solution of the problem. Thus the variational iteration method is suitable for finding the approximation of the solution without discretization of the problem. We change the main problem to a direct problem which is easy to handle the variational iteration method. To show the efficiency of the present method, several examples are presented. Also it is shown that this method coincides with Adomian decomposition method for the studied problem.

### MSC:

 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations 35R30 Inverse problems for PDEs
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