Numerical solution of Hammerstein integral equations in L_p spaces

• Autorzy: Nadir M. , Gagui B
• Języki publikacji: EN

Abstrakty

EN

In this work, we give conditions guarantee the boundedness of the Hammerstein integral operator in L_p spaces. The existence and the uniqueness of the solution of Hammerstein integral equation are treated under some assumptions affected to the successive approximation, so that we obtain the convergence of the approximate solution to the exact one. Finally, we treat numerical examples to confirm our results.

Słowa kluczowe

EN

hammerstein integral equation; successive approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 52
• Strony: 83--91
• Opis fizyczny: Bibliogr. 9 poz., tab.

Twórcy

autor

Nadir M.

• Department of Mathematics University of Msila 28000 Algeria

autor

Gagui B

• Department of Mathematics University of Msila 28000 Algeria

Bibliografia

• [1] Awawdeh F., Adawi A., A numerical method for solving nonlinear integral equations, International Mathematical Forum, 4(1)(2009), 805-817.
• [2] Ezzati R., Shakibi K., On approximation and numerical solution of Fredholm-Hammerstein integral equations using multiquadric quasi-interpolation, Communication in Numerical Analysis, 112(2012).
• [3] Kantorovitch L.,Akilov G., Functional analysis, Pergamon Press, University of Michigan, 1982.
• [4] Maleknejad K., Derili M., The collocation method for Hammerstein equations by Daubechies wavelets, Applied Mathematics and Computation, 172(2006), 846-864.
• [5] Maleknejad K., Nouri K., Nosrati M., Convergence of approximate solution of nonlinear Fredholm-Hammerstein integral equations, Commun Nonlinear Sci Numer Simulat, 15(2010), 1432-1443.
• [6] Nadir M., Gagui B., Two Points for the Adaptive Method for the Numerical Solution of Volterra Integral Equations, International Journal Mathematical Manuscripts (IJMM), 1(2)(2007).
• [7] Nadir M., Rahmoune A., Solving linear Fredholm integral equations of the second kind using Newton divided difference interpolation polynomial, International Journal of Mathematics and Computation (IJMC), 7(10)(2010), 1-6.
• [8] Szufla S., On the Hammerstein integral equation in Banach spaces, Math. Nachr., 124(1985), 7-14.
• [9] F.G. Tricomi, Integral Equations, University Press, University of Cambridge, 1957.