Öz In this study, a numerical method is developed for the approximate solution of the linear Volterra integro-differential equations. This method is based Boole polynomial, its derivatives and the collocation points. The aim is to reduce the given problem, as the linear algebraic equation, to the matrix equation. This matrix equation is solved using Boole collocation points. As a result, the approximate solution is obtained in the truncated Boole series in the interval [a,b]. The exact solution and the approximate solution are included in the study. Also, the error analysis and residual correction calculations are performed in the study. The results have been obtained by using computer program MATLAB.

Anahtar Kelimeler:
##
Boole polynomial,
linear Volterra integro-differential equation,
collocation points,
approximate solutions,
Residual error analysis

2. Laib, H, Bellour, A, Bousselsal, A. 2019. Numerical solution of high-order linear Volterra integro-differential equations by using Taylor collocation method. International Journal of Computer Mathematics; 96 (5): 1066–1085.

3. Chen, J, He, M, Zeng, T. 2019. A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation II: Efficient algorithm for the discrete linear system. J. Vis. Commun. Image R.; 58: 112–118.

4. Hesameddini, E, Shahbazi, M. 2019. Solving multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type using Bernstein polynomials Method. Applied Numerical Mathematics; 136: 122–138.

5. Rohaninasab, N, Maleknejad, K, Ezzati, R. 2018. Numerical solution of high-order Volterra–Fredholm integro-differential equations by using Legendre collocation method. Applied Mathematics and Computation; 328: 171–188.

6. Wang, Y, Zhu, L. 2017. Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method. Advances in Difference Equations; 2017(1): 27.

7. Babayar-Razlighi, B, Soltanalizadeh, B. 2013. Numerical solution for system of singular nonlinear Volterra integro-differential equations by Newton-Product method. Applied Mathematics and Computation; 219: 8375–8383.

8. Roul, P, Meyer, P. 2011. Numerical solutions of systems of nonlinear integro-differential equations by Homotopy-perturbation method. Applied Mathematical Modelling; 35: 4234–4242.

9. Yüzbaşı, Ş. 2016. Improved Bessel collocation method for linear Volterra integro-differential equations with piecewise intervals and application of a Volterra population model. Applied Mathematical Modelling; 40: 5349–5363.

10. Gu, Z. 2019. Spectral collocation method for weakly singular Volterra integro-differential equations. Applied Numerical Mathematics; 143: 263–275.

11. Yuzbasi, S, Sahin, N, Sezer, M. 2011. Bessel matrix method for solving high-order linear Fredholm integro-differential equations, Journal of Advanced Research in Applied Math.; 3(23): 1-25.

12. Hosseini, SM, Shahmorad, S. 2003. Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases. Applied Mathematical Modelling; 27: 145–154.

13. Erdem, Biçer, K, Sezer, M. 2017. Bernoulli matrix-collocation method for solving general functional integro- differential equations with Hybrid delays. Journal of Inequalities and Special Functions; 8(3): 85-99.

14. Turkyilmazoglu, M. 2014. An effective approach for numerical solutions of high-order Fredholm integro-differential equations. Appl. Math. Comput; 227: 384–398.

15. Kürkçü, ÖK, Aslan, E, Sezer, M. 2016. A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials. Applied Mathematics and Computation; 276: 324–339

16. Yıldırım, A. 2008. Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Computers and Mathematics with Applications; 56: 3175-3180.

17. Mirzaee, F, Hoseini, SF. 2017. A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients. Applied Mathematics and Computation; 311: 272–282.

18. Yalçınbaş, S, Erdem, K. 2014. A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations. Applied Mathematics and Physic; 2(2): 40-48.

19. Mustafa, MM, Muhammad, AM. 2014. Numerical Solution of Linear Volterra-Fredholm Integro-Differential Equations Using Lagrange Polynomials. Mathematical Theory and Modelin; 4(5): 137-146.

20. Dastjerdi, HL, Maalek, Ghaini FM. 2012. Numerical solution of Volterra–Fredholm integral equations by moving least square method and Chebyshev polynomials. Applied Mathematical Modelling; 36: 3283–3288.

21. Maleknejad, K, Basirat, B, Hashemizadeh E. 2012. A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations. Mathematical and Computer Modelling; 55: 1363–1372.

22. Yüzbaşı, Ş, Şahin, N, Yildirim, A. 2012. A collocation approach for solving high-order linear Fredholm–Volterra integro-differential equations. Mathematical and Computer Modelling; 55: 547–563. 23. Rashidinia, J, Tahmasebi, A. 2013. Approximate solution of linear integro-differential equations by using modified Taylor expansion method. World Journal of Modelling and Simulation; 9(4): 289-301.

24. Erdem, Bicer, K, Yalcinbas, S. 2016. A Matrix Approach to Solving Hyperbolic Partial Differential Equations Using Bernoulli Polynomials, Published by Faculty of Sciences and Mathematics, 30(4): 993–1000.

25. Cravero, I, Pittaluga, G, Sacripante, L. 2012. An algorithm for solving linear Volterra integro-differential equations. Numer Algor; 60: 101–114,

26. Jordan, C. Calculus of Finite Differences; Chelsea Publishing Company: New York, 1950; pp 318.

27. Baykus, Savasaneril, N, Sezer, M. 2016. Laguerre polynomial solution of high- order linear Fredholm integro-differential equations. NTMSCI; 4(2), 273-284.

28. Yüzbaşı, Ş, Şahin, N, Sezer, M. 2011. Bessel polynomial solutions of high-order linear Volterra integro-differential equations. Computers and Mathematics with Applications; 62: 1940–1956.

29. Balcı, MA, Sezer, M. 2016. Hybrid Euler-Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations. Applied Mathematics and Computation; 273: 33–41.

30. Roman, S., The Umbral Calculus; ACADEMIC PRESS: New York, 1984; pp 12.

31. Kim, DS. 2014. A note on Boole polynomials. Integral Transforms and Special Functions, 25(8): 627-633.

Bibtex | `@araştırma makalesi { cbayarfbe791302, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {}, publisher = {Celal Bayar Üniversitesi}, year = {2020}, volume = {17}, pages = {59 - 66}, doi = {10.18466/cbayarfbe.791302}, title = {Boole approximation method with residual error function to solve linear Volterra integro-differential equations}, key = {cite}, author = {Erdem Biçer, Kübra and Dağ, Hale Gül} }` |

APA | Erdem Biçer, K , Dağ, H . (2020). Boole approximation method with residual error function to solve linear Volterra integro-differential equations . Celal Bayar University Journal of Science , 17 (1) , 59-66 . DOI: 10.18466/cbayarfbe.791302 |

MLA | Erdem Biçer, K , Dağ, H . "Boole approximation method with residual error function to solve linear Volterra integro-differential equations" . Celal Bayar University Journal of Science 17 (2020 ): 59-66 <https://dergipark.org.tr/tr/pub/cbayarfbe/issue/60937/791302> |

Chicago | Erdem Biçer, K , Dağ, H . "Boole approximation method with residual error function to solve linear Volterra integro-differential equations". Celal Bayar University Journal of Science 17 (2020 ): 59-66 |

RIS | TY - JOUR T1 - Boole approximation method with residual error function to solve linear Volterra integro-differential equations AU - Kübra Erdem Biçer , Hale Gül Dağ Y1 - 2020 PY - 2020 N1 - doi: 10.18466/cbayarfbe.791302 DO - 10.18466/cbayarfbe.791302 T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 59 EP - 66 VL - 17 IS - 1 SN - 1305-130X-1305-1385 M3 - doi: 10.18466/cbayarfbe.791302 UR - https://doi.org/10.18466/cbayarfbe.791302 Y2 - 2021 ER - |

EndNote | %0 Celal Bayar Üniversitesi Fen Bilimleri Dergisi Boole approximation method with residual error function to solve linear Volterra integro-differential equations %A Kübra Erdem Biçer , Hale Gül Dağ %T Boole approximation method with residual error function to solve linear Volterra integro-differential equations %D 2020 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 17 %N 1 %R doi: 10.18466/cbayarfbe.791302 %U 10.18466/cbayarfbe.791302 |

ISNAD | Erdem Biçer, Kübra , Dağ, Hale Gül . "Boole approximation method with residual error function to solve linear Volterra integro-differential equations". Celal Bayar University Journal of Science 17 / 1 (Aralık 2020): 59-66 . https://doi.org/10.18466/cbayarfbe.791302 |

AMA | Erdem Biçer K , Dağ H . Boole approximation method with residual error function to solve linear Volterra integro-differential equations. Celal Bayar Univ J Sci. 2020; 17(1): 59-66. |

Vancouver | Erdem Biçer K , Dağ H . Boole approximation method with residual error function to solve linear Volterra integro-differential equations. Celal Bayar University Journal of Science. 2020; 17(1): 59-66. |

IEEE | K. Erdem Biçer ve H. Dağ , "Boole approximation method with residual error function to solve linear Volterra integro-differential equations", Celal Bayar University Journal of Science, c. 17, sayı. 1, ss. 59-66, Ara. 2021, doi:10.18466/cbayarfbe.791302 |

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