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

Iranian Journal of Numerical Analysis and Optimization

مقاله 7، دوره 9، شماره 1 - شماره پیاپی 15، 2019، صفحه 127-150   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v9i1.63182

نویسندگان

S. Pishbin^* ؛ J. Shokri

Urmia University, Urmia, Iran.

چکیده

‎‎ 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.

کلیدواژه‌ها

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

مراجع