Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method

• Autorzy: Henka Youcef , Lemita Samir , Aissaoui Mohamed-Zine

Identyfikatory

DOI

10.17512/jamcm.2022.4.03

• Języki publikacji: EN

Abstrakty

EN

In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.

Słowa kluczowe

EN

Fredholm integro-differential equations; nonlinear equation; Galerkin method; Chebyshev wavelets

PL

równanie całkowo-różniczkowe Fredholma; równanie nieliniowe; metoda Galerkina; falki Czebyszewa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 4
• Strony: 28--39
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Henka Youcef

• Laboratoire de Mathématiques Appliquées et de Modélisation. Université 8 Mai 1945 Guelma, B.P. 401 Guelma 24000, Algérie

autor

Lemita Samir

• Ecole Normale Supérieure de Ouargla. Cité Ennacer, Ouargla 30000, Algeria

autor

Aissaoui Mohamed-Zine

• Laboratoire de Mathématiques Appliquées et de Modélisation. Université 8 Mai 1945 Guelma, B.P. 401 Guelma 24000, Algérie

Bibliografia

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• [6] Kumbinarasaiah, S., & Mundewadi, R.A. (2021). The new operational matrix of integration for the numerical solution of integro-differential equations via Hermite wavelet. SeMA Journal, 78(3), 367-384.
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• [10] Avudainayagam, A., & Vani, C. (2000). Wavelet-Galerkin method for integro-differential equations. Applied Numerical Mathematics, 32(3) 247-254.
• [11] Shiralashetti, S.C., & Kumbinarasaiah, S. (2019). Laguerre wavelets collocation method for the numerical solution of the Benjamina-Bona-Mohany equations. Journal of Taibah University for Science, 13(1), 9-15.
• [12] Bahuguna, D., Ujlayan, A., & Pandey, D.N. (2009). A comparative study of numerical methods for solving an integro-differential equation. Computers & Mathematics with Applications, 57(9), 1485-1493.
• [13] Biҫer, G.G., Öztürk, Y., & Gülsu, M. (2018). Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials. International Journal of Computer Mathematics, 85(10), 2100-2111.
• [14] Pittaluga, G., & Sacripante, L. (2009). An algorithm for solving Fredholm integro-differential equations. Numerical Algorithms, 50(2), 115-126.
• [15] Mahmoodi, Z., Rashidinia, J., & Babolian, E. (2013). B-Spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations. Applicable Analysis, 92(9), 1787-1802.
• [16] Al-Khaled, K. (2002). On the rate of convergence for the Chebyshev series. Missouri Journal of Mathematical Sciences, 14(1), 4-10.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).