# CUBIC MECHANICAL METHOD FOR THE NONLINEAR SYSTEM OF SINGULAR INTEGRAL EQUATIONS

## Authors

• R. P. Eissa Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
• M. M. Gad Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.

## Keywords:

cubic mechanical method, nonlinear system, singular integral equations, method of iterated approxima- tion, speed of convergence

## Abstract

Many applied problems in the theory of elasticity can be reduced to the solution of singular integral equations either linear or nonlinear. In this paper we shall study a nonlinear system of singular integral equations which appear on the closed Lipanouv surface in an ideal medium . We shall find a cubic mechanical method which corresponds to the system and prove its convergence; we obtained a discrete operator which corresponds to this system and study its properties and then a solution to the resulting system of the nonlinear equations which leads to an approximate solution for the original system and its convergence.

## References

R. P. Eissa, Cubic Mechanical Method for one class of nonlinear singular integral Equations "I", Bulletin of the Faculty of Engineering, Ain Shams University, No 17, 1985.

R. P. Eissa, Cubic Mechanical Method for one of nonlinear singular integral Equations "II", B ulletin of the Faculty of Engineering, Ain Shams University, No 17, 1985.

E. A. EsKovetch, The equivalence problems to the theory of two dimensional singular equation, chen. Zap. Keshenofa Univ. No 5, 1952.

E. A. EsKovetch and A. K. Kolocoveskaya, The three dimensional Problems on the flowing of an ideal liquid with simple barrier. Chen. Zap. I(eshenofa Univ. No 11, 1954.

U. A. Kostof and B. A. Mossaef, Cubic formulae for two dimensional singularintegrals and its application. Dep. in VINITI No. 4281, 1981.

1990-09-01

## How to Cite

Eissa, R. P., & Gad, M. M. (1990). CUBIC MECHANICAL METHOD FOR THE NONLINEAR SYSTEM OF SINGULAR INTEGRAL EQUATIONS. Tamkang Journal of Mathematics, 21(3), 201–209. https://doi.org/10.5556/j.tkjm.21.1990.4659

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