Regularization technique and numerical analysis of the mixed system of first and second-kind Volterra–Fredholm integral equations

• Published in: Iranian journal of numerical analysis and optimization Vol. 9; no. 1; pp. 127 - 150
• Main Authors: S. Pishbin, J. Shokri
• Format: Journal Article
• Language: English
• Published: Ferdowsi University of Mashhad 01.03.2019
• Subjects: chebyshev wavelets; convergence ‎analysis; mixed systems of first and second-kind volterra-fredholm integral ‎equations; regularization‎ ‎method
• ISSN: 2423-6977; 2423-6969
• DOI: 10.22067/ijnao.v9i1.63182

‎‎ It is important to note that mixed systems of first and second-kind Volterra–Fredholm integral equations are ill-posed problems, so that solving discretized system of such problems has a lot of difficulties. We will apply the regularization method to convert this mixed system (ill-posed problem) to system of the second kind Volterra–Fredholm integral equations (well-posed problem). A numerical method based on Chebyshev wavelets is suggested for solving the obtained well-posed problem, and convergence analysis of the method is discussed. For showing efficiency of the method, some test problems, for which the exact solution is known, are considered.