Numerical Treatment of Volterra integral Equation of the 2nd kind Using 6th order of Runge-Kutta method

DOI:

https://doi.org/10.31695/IJERAT.2020.3673

Keywords:

General 2ndorder of non-linear Volterra integral equation, 6th order Improved Range-Kutta methods

Abstract

The aim of this paper is to study and to obtain an approximate solution of non-linear Volterra integral equation of the second kind ,the researcher implemented the modified method by using specific examples involving volterra integral equation to show the capability and efficiency of our approximate method according to the exact solution in addition to the ease in programming the approximate method 

References

Miller, R.K. (1967), Nonlinear Volterra Integral Equations ,W. A. Benjamin, Menlo Park,

Matoog,R.T. (2014), Numerical Treatment for solving Nonlinear Volterra Integral Equation of the second kind ,Journal of Applied Mathematics & Bioinformatics, Vol.4, No.1, 33-43.

Chen L., Duna ,J. Sh. (,2015) , Numerical Picard Iteration methods for Nonlinear Volterra Integral Equations of the second kind, Advances in Pure Mathematics, Vol.5,pp 672-682.

https://dx.doi.org/10.4236/apm.2015.

Rahman, M .M. Hakim, M.A. (2012),Numerical solutions of Volterra Integral Equations of the second kind with the help of Chebchev Polynomials,Annals of Pure and Applied Mathematics,Vol.1,No.2, pp158-167.

Ramm ,A. (2008) A Collocation method for solving Integral Equations ,Int.J.Computing Science & Mathematics,Vol.48,No.10.

Xie,L.J.,‘A New Modification of A domain Decomposition Method for Volterr Integral Equations of the second kind ,Hindawi Publishing Corporation,Journal of Applied Mathematics,2013.

http://dx.doi.org/10.1155/2013/795015.

Brunner,H. , Hairer E. & Njersett,S.P.( 1982), Runge-Kutta Theory for Volterra Integral Equations of The Second Kind ,Mathematics of Computation ,Vol39,No159, pp147-163.

Malek nejad, K., Shahrezaee ,M.( (2004) ,Using Runge-Kutta Method for Numerical Solution of The System of Volterra Integral Equations, Appl. Math. Comput.149399-410.

Capobianco,G., Conte D., Prete I.Dell & Russo, E.( 2007 ) , Fast Runge –Kutta Methods for Nonlinear Convolution System of Volterra Integral Equations, BIT, ,V.47,pp259-275.

Mustafa, M.M. (2010)., Volterra Runge-Kutta Methods for Solving Nonlinear Volterra Integral Equation ,Baghdad Science Journel, V.7,N.3,PP.1270-1274.

Bijan H.Lich, A Class of Runge-Kutta Methods for Nonlinear Volterra Integral Equation of the second kind with Singular Kernels”, Lichae et al. Advances in Difference Equations,2018,pp2-19.

https://doi.org/10.1186/s13662-018-1811-8.

Jerri, A. (1999) Intruduction to Integral Equations with Application ,Wiley,NewYork.

Runge, Carl David Tolmé (1895), Über die numerische Auflösung von Differential gleichungen , Mathematische Annalen, Springer, Vol .46 No. 2,PP 167–178, doi:10.1007/BF01446807.

Goeken, D. , Johnson,O. (2000) ,Runge-Kutta with Higher Order Derivative Approximations, Appl . Numer.Math,34, ,PP 207-218.

Butcher, J.C, (1964) On Runge-Kutta Processes of High Order, ,J.Australia n.Math,Soci.4, ,PP 179-194.

Dr. Al-Faour ,O. M ., .Mustafe ,M .M and Al-Rawi S. N.( 2002), Numerical Treatment of Non-Linear Volterra Integral Equations Using Runge-Kutta Methods, Journal of Al-Rafidain University College For Science, No.11,PP114-124,.

Delves,L , Mohammad, J.( ,(1988) ,Computational Methods for Integral Equations ,Cambridge University Press

Saleh ,A.J. , Esa, R.I. & Jameel ,A.F. (2019), Numerical Treatment of Non-linear Volterra Integrao –Differential Equation using Runge-Kutta Methods, AIP Conference Proceedings 2138,030034.

https://doi.org/10.1063/1.5121071.

Abbas ,A.F.( 2017) ,Solving Initial Value Problem Using Runge-Kutta 6th order Method, ARPN Journal of Engineering and Applied Sciences, Vol.12,No.13,pp3953-3960. www.arpnjournals.com.

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Numerical Treatment of Volterra integral Equation of the 2nd kind Using 6th order of Runge-Kutta method. (2020). International Journal of Engineering Research and Advanced Technology (ijerat) (E-ISSN 2454-6135) DOI: 10.31695/IJERAT, 6(12), 17–23. https://doi.org/10.31695/IJERAT.2020.3673

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