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

Document Type : Research Article

Authors

• S. Pishbin
• J. Shokri

Urmia University, Urmia, Iran.

10.22067/ijnao.v9i1.63182

Abstract

‎‎ 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.

Keywords

• Mixed systems of first and second-kind Volterra-Fredholm integral ‎equations‎
• ‎Regularization‎ ‎method‎
• Chebyshev wavelets
• ‎Convergence ‎analysis‎‎

20.1001.1.24236977.2019.9.1.7.0

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