Solving linear Fredholm integro-differential equation by Nyström method

• Autorzy: Tair Boutheina , Guebbai Hamza , Segni Sami , Ghiat Mourad

Identyfikatory

DOI

10.17512/jamcm.2021.3.05

• Języki publikacji: EN

Abstrakty

EN

The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C¹ [a,b]. We have applied the Nyström method based on the trapezoidal rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.

Słowa kluczowe

EN

Fredholm integral equation; system of integral equations; integro-differential equations; Nyström method

PL

równanie całkowe Fredholma; układ równań całkowych; równanie całkowo-różniczkowe; metoda Nyströma

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 3
• Strony: 53--64
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Tair Boutheina

• Laboratoire des Mathématiques Appliquées et Modélisation, Université 8 Mai 1945 Guelma 24000, Algeria

autor

Guebbai Hamza

• Laboratoire des Mathématiques Appliquées et Modélisation, Université 8 Mai 1945 Guelma 24000, Algeria

autor

Segni Sami

• Laboratoire des Mathématiques Appliquées et Modélisation, Université 8 Mai 1945 Guelma 24000, Algeria

autor

Ghiat Mourad

• Laboratoire des Mathématiques Appliquées et Modélisation, Université 8 Mai 1945 Guelma 24000, Algeria

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).