A variational form with Bernoulli series for linear integral equations

• Autorzy: Nadir M.
• Języki publikacji: EN

Abstrakty

EN

In this work, we seek the approximate solution of Fredholm integral equations by truncation Bernoulli series approximation using a variational form for the equation. This one is reduced to a linear system where the solution of this latter gives the Bernoulli coefficients and thereafter the solution of the equation.The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

Słowa kluczowe

EN

linear integral equations; Bernoulli polynomials; collocation methods

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Journal of Theoretical and Applied Computer Science
• Rocznik: 2014
• Tom: Vol. 8, nr 3
• Strony: 31--36
• Opis fizyczny: Bibliogr. 9 poz., tab.

Twórcy

autor

Nadir M.

• Department of Mathematics, University of Msila, Algeria

Bibliografia

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• [2] Beny, N., Nelson, P.: Adaptive Method for the Numerical Solution of Fredholm Integral Equations of the Second Kind, Part I Regular Kernels. In: Gerasoulis, A., Vichnevetsky, R. (eds.) Numerical Solution of Singular Integral Equations, pp. 68–72, 1984.
• [3] Chakrabarti, A., Martha, S. C.: Approximate solutions of Fredholm integral equations of the second kind. Applied Mathematics and Computation, 211, pp. 459–466, 2009.
• [4] Kress, R.: Linear Integral Equations. Springer-Verlag, Berlin, Heidelberg, 1989.
• [5] Maleknejad, K., Aghazadeh, N.: Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. Applied Mathematics and Computation, 161, pp. 915–922, 2005.
• [6] Mirzaee, F.: Numerical Solution for Volterra Integral Equations of the First Kind via Quadrature Rule. Applied Mathematical Sciences, Vol. 6, No. 20, pp. 969–974, 2012.
• [7] Nadir, M.: Solving Fredholm integral equations with application of the four Chebyshev polynomials. Journal of Approximation Theory and Applied Mathematics, 4, pp. 37–44, 2014.
• [8] Nadir, M., Rahmoune, A.: Modified Method for Solving Linear Volterra Integral equations of the Second Kind Using Simpson’s Rule. International Journal Mathematical Manuscripts (IJMM), 1(2), pp. 133–140, 2007.
• [9] Yalçınbaş, S., Aynigül, M.: Hermite series solutions of linear Fredholm integral equations. Mathematical and Computational Applications, Vol. 16, No. 2, pp. 497–506, 2011.