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Fredholm İntegro Diferansiyel Denklemin Sayısal Çözümü için Alternatif Bir Yöntem

Yıl 2020, Cilt: 13 Sayı: 1, 46 - 53, 20.03.2020
https://doi.org/10.18185/erzifbed.633899

Öz

Bu çalışmada, birinci mertebeden
lineer Fredholm integro diferansiyel denklem için başlangıç değer problemini
ele alıyoruz. Bu problemin nümerik çözümü için düzgün şebekede bir yeni fark
şeması inşa ediyoruz. Bu şema, kalan terimi integral biçiminde olan
interpolasyon quadratür formülleri ve üstel baz fonksiyonunu içeren integral
özdeşliklerinden meydana gelmektedir. Metodun ayrık maksimum normda birinci
mertebeden yakınsaklığı ispatladık. Ayrıca, hem sunulan metot hem de Euler
metodu kullanılarak bir örnek çözüldü ve hesaplanan sonuçlar kaşılaştırıldı.

Kaynakça

  • Amiraliyev G. M., Durmaz M. E., Kudu M. 2018. “Uniform convergence results for singularly perturbed Fredholm integro-differential equation”, J. Math. Anal. 9(6), 55-64.
  • Amiraliyev G. M., Mamedov Y. D. 1995. “Difference schemes on the uniform mesh for a singularly perturbed pseudo-parabolic equations”, Tr. J. Math. 22, 202-222.
  • Arqub O. A., Al-Smadi M., Shawagfeh N. 2013. “Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method”, Appl. Math. Comput. 219, 8938-8948.
  • Bloom F. 1980. “Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory”, J. Math. Anal. Appl. 73, 524-542.
  • Çimen E. 2018. “A computational method for Volterra integro-differential equation”, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 11(3), 347-352.
  • Darania P., Ebadian A. 2007. “A method for the numerical solution of the integro-differential equations”, Appl. Math. Comput. 188(1), 657-668.
  • Forbes L. K., Crozier S., Doddrell D. M. 1997. “Calculating current densities and fields produced by shielded magnetic resonance imaging probes”, SIAM J. Appl. Math. 57, 401-425.
  • Hackbusch W. (1995). “Integral Equations Theory and Numerical Treatment”, Birkhauser, Basel.
  • Holmaker K. 1993. “Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones”, SIAM J. Math. Anal. 24, 116-128.
  • Jerri A. (1999). “Introduction to Integral Equations with Applications”, Wiley, New York.
  • Kythe P. K., Puri P. (2002). “Computational Methods for Linear Integral Equations”, Springer, New York.
  • Medlock J., Kot M. 2003. “Spreading disease: integro-differential equations old and new”, Math. Biosciences. 184, 201-222.
  • Rahman M. (2007). “Integral Equations and Their Applications”, WIT Press, Boston.
  • Volterra V. (1959). “Theory of Functionals and of Integral and Integro-differential Equations”, Dover Publications, New York.
  • Wazwaz A. M. (2011). “Linear and Nonlinear Integral Equations Methods and Applications”, Springer, Berlin.
  • Yapman Ö., Amiraliyev G. M., Amirali I. 2019. “Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay”. J. Comput. Appl. Math. 355, 301-309.

An Alternative Method for Numerical Solution of Fredholm Integro Differential Equation

Yıl 2020, Cilt: 13 Sayı: 1, 46 - 53, 20.03.2020
https://doi.org/10.18185/erzifbed.633899

Öz

In this
paper, we consider a linear first order Fredholm integro differential equation
with initial condition. To solve this problem numerically, we construct a

new difference scheme on a uniform mesh. The scheme is based on the method of
integral identities with the use of exponential basis functions and
interpolating quadrature rules with the weight and remainder terms in integral
form. We prove that the method is

first order convergence in the discrete maximum norm. Moreover, a numerical
example is solved using both the presented method and the Euler method and
compared the computed results.

Kaynakça

  • Amiraliyev G. M., Durmaz M. E., Kudu M. 2018. “Uniform convergence results for singularly perturbed Fredholm integro-differential equation”, J. Math. Anal. 9(6), 55-64.
  • Amiraliyev G. M., Mamedov Y. D. 1995. “Difference schemes on the uniform mesh for a singularly perturbed pseudo-parabolic equations”, Tr. J. Math. 22, 202-222.
  • Arqub O. A., Al-Smadi M., Shawagfeh N. 2013. “Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method”, Appl. Math. Comput. 219, 8938-8948.
  • Bloom F. 1980. “Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory”, J. Math. Anal. Appl. 73, 524-542.
  • Çimen E. 2018. “A computational method for Volterra integro-differential equation”, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 11(3), 347-352.
  • Darania P., Ebadian A. 2007. “A method for the numerical solution of the integro-differential equations”, Appl. Math. Comput. 188(1), 657-668.
  • Forbes L. K., Crozier S., Doddrell D. M. 1997. “Calculating current densities and fields produced by shielded magnetic resonance imaging probes”, SIAM J. Appl. Math. 57, 401-425.
  • Hackbusch W. (1995). “Integral Equations Theory and Numerical Treatment”, Birkhauser, Basel.
  • Holmaker K. 1993. “Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones”, SIAM J. Math. Anal. 24, 116-128.
  • Jerri A. (1999). “Introduction to Integral Equations with Applications”, Wiley, New York.
  • Kythe P. K., Puri P. (2002). “Computational Methods for Linear Integral Equations”, Springer, New York.
  • Medlock J., Kot M. 2003. “Spreading disease: integro-differential equations old and new”, Math. Biosciences. 184, 201-222.
  • Rahman M. (2007). “Integral Equations and Their Applications”, WIT Press, Boston.
  • Volterra V. (1959). “Theory of Functionals and of Integral and Integro-differential Equations”, Dover Publications, New York.
  • Wazwaz A. M. (2011). “Linear and Nonlinear Integral Equations Methods and Applications”, Springer, Berlin.
  • Yapman Ö., Amiraliyev G. M., Amirali I. 2019. “Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay”. J. Comput. Appl. Math. 355, 301-309.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Erkan Cimen 0000-0002-7258-192X

Kübra Enterili Bu kişi benim 0000-0001-5318-9642

Yayımlanma Tarihi 20 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 13 Sayı: 1

Kaynak Göster

APA Cimen, E., & Enterili, K. (2020). Fredholm İntegro Diferansiyel Denklemin Sayısal Çözümü için Alternatif Bir Yöntem. Erzincan University Journal of Science and Technology, 13(1), 46-53. https://doi.org/10.18185/erzifbed.633899