Convergence analysis of a highly accurate Nyström scheme for Fredholm integral equations
Source of Publication
Applied Numerical Mathematics
© 2019 IMACS A stable and convergent Nyström scheme is proposed to solve Fredholm integral equations (FIEs). Our approximation is based on the barycentric rational interpolants. By introducing barycentric quadratures to the integral operator that appears in the FIE and modifying the standard Nyström scheme, we demonstrate that the new Nyström scheme is a viable option for the numerical solution of FIEs. Convergence rates of the method are proved taking into account the effect of grading the domain. The final convergence result shows clearly that one can choose an optimal domain grading. Numerical examples and comparisons with competitive methods of tunable accuracy are provided to support the theoretical analysis and illustrate the efficiency of the proposed numerical scheme.
Barycentric rational interpolation, Convergence analysis, Fredholm integral equations, Nyström method
Awawdeh, Fadi and Smail, Linda, "Convergence analysis of a highly accurate Nyström scheme for Fredholm integral equations" (2020). All Works. 1082.
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