In this paperwe have considered an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. This equation contains variable coefficients with large expressions which complicate the application of any numerical method. We have used variational iteration method to find its numerical solution by developing MATHEMATICA modulae and solved a number of numerical examples. The results show high accuracy and efficiency ofour approach.

Many physical phenomena can be modeled by partial differential equations with singularities and interfaces. The standard finite difference and finite element methods may not be successful in giving satisfactory numerical results for such problems. Hence, many new methods have been developed. Some of them are developed with the modifications in the standard methods, so that they can deal with the discontinuities and the singularities. In this article, a survey has been done on some recent efficient techniques to solve elliptic interface problems.

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