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APPROXIMATE AND STABILITY SOLUTION FOR NON-LINEAR SYSTEM OF INTEGRODIFFERENTIAL EQUATIONS OF VOLTERRA TYPE WITH BOUNDARY CONDITIONS

Raad Noori Butris(1), Noori R Noori(2),


(1) (SCOPUS ID : 16427511100, College of Basic Education, Department of Mathematics, University of Duhok)
(2) Duhok Polytechnic University, College of Engineering, Department of Energy
Corresponding Author

Abstract


In this paper, we investigate the approximation and stability solutions of non-linear systems of integro-differential equations of Volterra type with boundary conditions, by using the numerical-analytic method which were introduced by Samoilenko. The study of such integro-differential equations leads to extend the results obtained by Butris for changing the system of non-linear integro- differential equations of Volterra type to the system of non-linear integro-differential equations of the Volterra type with boundary conditions. Theorems on a solutions are established under some necessary and sufficient conditions on compact spaces.

Keywords


Numerical-analytic method, Volterra integro-differential equations, Boundary conditions, Periodic solutions

References


Ali, A. R. , Periodic solutions for some classes of non-linear systems of integrodifferential equations, M. Sc. Thesis, college of Science, Duhok University, Duhok, (2010),

Aziz, M. A. , Periodic solutions for some systems of non-linear ordinary differential

equations, M. Sc. Thesis, College of Education, University of Mosul, (2006).

Butris, R. N. , Periodic solution of non-linear system of Integro - differential equations

depending on the Gamma distribution, India, Gen. Math . Notes Vol.15, No.1, (2013). pp.56 -

,

Butris, R. N. , Periodic solution for a system of second-order differential equations with

boundary integral conditions, Univ. of Mosul, J. of Educ and Sci. Vol. 18. (1994).

Butris, R. N. , Periodic Solution for Non-linear System of Integro-differential

Equations Of Volterra Type, International Journal of Scientific Engineering and Applied

Science (IJSEAS) – Vol 1, Issue 5, (2015).pp 88-112.

Benaicha, S. , Periodic boundary value problems for second order ordinary differential

equations, University of Oran , Es-senia, Algeria, Applied Mathematical Sciences, Vol. 3,

No.6, , (2009 pp.267-276).

James, R. W. , Periodic solution of ordinary differential equations with boundary

nonlinearities, J. of the Julius Schauder Center Vol. 19, (2002). pp. 257-282

Mitropolsky, Yu. A. and Martynyuk, D. I. , For Periodic Solutions For the Oscillations

System with Retarded Argument, Kiev , Ukraine, General School (1979).

Narjanov, O. D. , On a Periodic solution for integro-differential equation, Math. J. ,

Kiev, Ukraine, Tom.2. (1977).

Naima, D. M. , Periodic solution of non-autonomous second–order differential

equations and boundary value problem, India, Issue. 6. (1999).

Perestyuk, N. A. and Martynyuk, D. I., Periodic solutions of a certain class systems of

differential equations, Math. J. Univ. of Kiev, Kiev, Ukraine, Tom 3, pp.146-156, (1976).

Putertnka, T. V. , The convergent method for non linear system of differential

equation with boundary integral conditions, Nonlinear problems in the theory of differential

equations J. Akad Nauk, Ukraine, Tom.9, pp.66-73, (1991).

Robert, M. M. and Robert. D. R. , Numerical Solution of Boundary Value Problem for

Ordinary Differential Equations, SIAM, In Applied Mathematics, United of America, (1988).

Rafeq, A. Sh. , Periodic solutions for non-linear systems of differential equations with

matrices, J. Duhok Univ. Vol. 14, No. 1,(2013) ,PP. 57-74.

Rafeq, A. Sh. , Periodic solutions for some of non-linear systems of integro –

differential equations, M. Sc. Thesis, college of Science, Duhok University, Duhok, (2009).

Ronto, A . , Ronto, M. and Shchobak, N. ,On numerical – analytic methods techniques

for boundary value problem, Acta Electrotechnica et Informatica, Vol.12, No. 3, pp.67-72,

DOI: 10.2478/v10198-012--0035-1, (2012).

Ronto, A . and Ronto, M. , On the investigation of some boundary value problems

with non- linear conditions, Mathematical Notes, Miskolc, Vol.1, No.1, (2000),pp.43-55.

Shslapk, Yu. D. , Periodic solution of first order nonlinear differential equations

unsolvable for the derivation, Math. J. Ukraine, Kive , Ukraine, Tom 5, pp. 850-854, (1980).

Samoilenko, A. M. and Ronto, N. I., A Numerical – Analytic Methods for Investigating

of Periodic Solutions, Kiev, Ukraine, (1976) .

Samoilenko, A. M. , A numerical – analytic methods for Successive approximation of

the problem with boundary integral condition, Kiev, Ukraine, Math. J. No. 9, (1991).

Samoilenko, A. M. and Ronto, N. I. , Numerical – Analytic Methods for Investigating

Solutions of Boundary Value Problem, Kiev, Ukraine, (1985).

Savun, I , Stability of systems of differential equation and biological Applications, M.

Sc. Thesis, Eastern Mediterranean University, Gazimağusa, North Cyprus, (2010).

Zavizion, G.V. , Periodic solutions of integro-differential equations, J. of Diff.

Equations, Vol.45, No. 2,(2009), pp.240-248.

Zafer, A. , Differential Equations and Their Applications, Second Edition, New Delhi, (2010).


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DOI: 10.56327/ijiscs.v7i2.1482

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