Lucas polynomials for solving linear integral equations

• Autorzy: Nadir M.
• Języki publikacji: EN

Abstrakty

EN

In this work, we seek the approximate solution of Fredholm and Volterra integral equations using Lucas polynomials and a given test functions, in order to reduce those equations to a linear system where its solution is to find the Lucas coefficients and thereafter the solution of the equation.The convergence of this method is assured and the error is compared with other methods.

Słowa kluczowe

EN

linear integral equations; Lusas polynomials; collocation methods; Sloan approximation

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Journal of Theoretical and Applied Computer Science
• Rocznik: 2017
• Tom: Vol. 11, nr 1
• Strony: 13--19
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Nadir M.

• Department of Mathematics, University of Msila, Algeria

Bibliografia

• [1] S. Abbasbandy, E. Shivanian, A new analytical technique to solve Fredholm’s integral equations, in Numer Algor 56, (2011), 27–43
• [2] A. Chakrabarti, S. C. Martha, Approximate solutions of Fredholm integral equations of the second kind, in Applied Mathematics and Computation 211, (2009), 459–466
• [3] P. Filipponi, A. F. Horadam, Derivative sequences of Fibonacci and Lucas polynomials, in Applications of Fibonacci Numbers 4,(1991), 99-108.
• [4] K. Maleknejad, N. Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. 161, (2005), 915–922.
• [5] K. Maleknejad, M. T. Kajani, Y. Mahmoudi, Numerical solution of linear Fredholm and Volterra integral equtions of the second kind using Legendre wavelets, in Journal of Sciences, Islamic Republic of Iran 13(2), (2002), 161-166.
• [6] M. Nadir, Solving Fredholm integral equations with application of the four Chebyshev polynomials, in Journal of Approximation Theory and Applied Mathematics 4, ( 2014), 37-44.
• [7] M. Nadir, A variational form with Bernoulli series for linear integral equations, in Journal of Theoretical and Applied Computer Science. 8(3) (2014), 31–36.
• [8] M. Nadir, M. Chemcham, Numerical solution of linear integral equations using hat function basis, in Asian Journal of Mathematics and Computer Research. 15 (1) (2017), 1-8.
• [9] M. Nadir, M. Dilmi, Euler series solutions for linear integral equations, in The Australian Journal of Mathematical Analysis and Applications. 14(2), (2017), 1-7.
• [10] M. Nadir, B. Lakehali, A variational form with Legendre series for linear integral equations, in Malaya Journal of Matematik. 6(1), (2018), 49-52.
• [11] M. A. Ramadan, M. R. Ali, An efficient hybrid method for solving fredholm integral equations using triangular functions, in NTMSCI 5(1), (2017), 213-224.
• [12] S. Yalc¸ınbas¸,MAynig¨ul, Hermite series solutions of linear Fredholm integral equations, in Mathematical and Computational Applications, 16(2), (2011), 497-506.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).