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

‎‎ 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)...

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Published inIranian journal of numerical analysis and optimization Vol. 9; no. 1; pp. 127 - 150
Main Authors S. Pishbin, J. Shokri
Format Journal Article
LanguageEnglish
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
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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.
AbstractList ‎‎ 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.
Author S. Pishbin
J. Shokri
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Snippet ‎‎ 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...
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StartPage 127
SubjectTerms chebyshev wavelets
convergence ‎analysis
mixed systems of first and second-kind volterra-fredholm integral ‎equations
regularization‎ ‎method
Title Regularization technique and numerical analysis of the mixed system of first and second-kind Volterra–Fredholm integral equations
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