# Numerical Solution of Linear Integral and Integro-Differential Equations Using Boubakar Collocation Method

Keywords:
Integral equations, Fredholm-Volterra integro-differential equations, Collocation method, Boubakar polynomial

### Abstract

This paper discusses a new collocation method based on Boubakar approximating polynomial for the solution of first order linear integral and integro-differential equations with initial condition. The integro-differential equations is converted into integral equations and later transformed to system of linear equations using standard collocation method. The linear equation is then solved using matrix inversion method. Three examples are given, numerical solutions show that the method is efficient in handling problems under consideration.

### References

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A. M. S. Mahdy, E. M. H. Mohammed, On the numerical solution of Hammerstein integral equations using shifted Chebyshev polynomial of the third kind method, NTMSCI , 5( 3 ) ,273-283, 2017

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C. Ercan, T. Khaterah,Solving a class of Volterra integral system by the differential transform method. Int. J. Nonlinear Sci. , 16( 1 ) , 87-91, 2013

A. M. Wazwaz, S. M. El-Sayed, A new modication of the Adomian decomposition method for linear and nonlinear operators, Appl. Math. Comput. , 122 , 393-404, 2001

A. Akyuz-Dasciouglu, A Chebyshev polynomial approach for linear Fredholm Volterra integro differential equations in the most general form, Appl. Math. Comput. , 181 , 103-112, 2006

A. H. Bhraway, E. Tohidi, F. Soleymani, A new Bernoulli matrix method for solving high order linear and nonlinear Fredholm integro differential equations with piecewise interval, Appl. Math. Comput. , 219 , 482-497, 2012

Berstein operational matrix approach for integro-differential equations arising in control theory, Nonlinear Engineering , 3( 2 ) , 117-123, 2014

M. El-kady, M. Biomy, Efficient Legendre pseudospectral method for solving integral and integro dierential equation, Commom. Nonlinear Sci. Numer. Simulat. , 1724-1739, 2010

S. Davaeifar, J. Rashidinia, Boubaker polynomials collocation approach for solving systems of nonlinear VolterraFredholm integral equations. Journal of Taibah University for Science , 11( 6 ) , 1182-1199, 2017 doi:10.1016/j.jtusci.2017.05.002

M. Rahman, Integral equations and their applications , Southampton, Boston, WIT press, 2007

G. Mehdiyera, M. Imanova, V. Ibrahim, Solving Volterra integro differential equation by second derivative methods. Appl. Math. Inf. Sci ., 9 (5), 2521-2527, 2015

S. Bhalekar, J. Patade, A novel third order numerical method for solving Volterra integro-differential equations. a.xiv:1604.08863vi, 2016

D. A. Gegele, O. P., Evans, D. Akoh, Numerical solution of higher order linear Fredholm integro-differential equations. American Journal of Engineering Research , 8( 3 ) , 243-247, 2014

M. K. Shahooth, R. Ahmad, U. Salman, W. Swidan, O. K. Al-Husseini, et. al ., Approximation solution of solving linear Volterra Fredholm integro differential equations of the second kind by using Berstein polynomial method, J. Appl. Computat. Math. , 5 (298), 2016, doi:10.

41721/2168-9678.1000298.

S. Nemati, P. Lima, Y. Ordokhani, Numerical method for the mixed Volterra Fredholm integral equation using hybrid Legendre function. Conference Application of Mathematics, 184-192, 2015

R. Katani, S Shahmorad, Block by block method for the systems of nonlinear Volterra integral equations. Applied Mathematical Modelling , 34 , 400-406, 2010

A. M. S. Mahdy, E. M. H. Mohammed, On the numerical solution of Hammerstein integral equations using shifted Chebyshev polynomial of the third kind method, NTMSCI , 5( 3 ) ,273-283, 2017

K. Issa, F. Saleh, Approximate solution of perturbed Volterra Fredholm integro differential equation by Chebyshev-Galerkin method. Journal of Mathematics, 2017 , doi:10.1155/2017/8213932

C. Ercan, T. Khaterah,Solving a class of Volterra integral system by the differential transform method. Int. J. Nonlinear Sci. , 16( 1 ) , 87-91, 2013

A. M. Wazwaz, S. M. El-Sayed, A new modication of the Adomian decomposition method for linear and nonlinear operators, Appl. Math. Comput. , 122 , 393-404, 2001

A. Akyuz-Dasciouglu, A Chebyshev polynomial approach for linear Fredholm Volterra integro differential equations in the most general form, Appl. Math. Comput. , 181 , 103-112, 2006

A. H. Bhraway, E. Tohidi, F. Soleymani, A new Bernoulli matrix method for solving high order linear and nonlinear Fredholm integro differential equations with piecewise interval, Appl. Math. Comput. , 219 , 482-497, 2012

Berstein operational matrix approach for integro-differential equations arising in control theory, Nonlinear Engineering , 3( 2 ) , 117-123, 2014

M. El-kady, M. Biomy, Efficient Legendre pseudospectral method for solving integral and integro dierential equation, Commom. Nonlinear Sci. Numer. Simulat. , 1724-1739, 2010

S. Davaeifar, J. Rashidinia, Boubaker polynomials collocation approach for solving systems of nonlinear VolterraFredholm integral equations. Journal of Taibah University for Science , 11( 6 ) , 1182-1199, 2017 doi:10.1016/j.jtusci.2017.05.002

M. Rahman, Integral equations and their applications , Southampton, Boston, WIT press, 2007

Published

2020-01-30

How to Cite

*International Journal of Mathematical Analysis and Optimization: Theory and Applications*,

*2019*(2), 592 - 598. Retrieved from http://ujh.unilag.edu.ng/index.php/ijmao/article/view/566

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