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Application of the variational iteration method to inverse heat source problems. (English) Zbl 1189.65216
Summary: This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. The numerical solution is developed by using the variational iteration method. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional. Using this method a rapid convergent sequence can be obtained which tends to the exact solution of the problem. Furthermore, the variational iteration method does not require the discretization of the problem. Thus the variational iteration method is suitable for finding the approximation of the solution without discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.

MSC:
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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