Abstract
We study two methods for solving a univariate Fredholm integral equation of the second kind, based on (left and right) partial approximations of the kernel K by a discrete quartic spline quasi-interpolant. The principle of each method is to approximate the kernel with respect to one variable, the other remaining free. This leads to an approximation of K by a degenerate kernel. We give error estimates for smooth functions, and we show that the method based on the left (resp. right) approximation of the kernel has an approximation order O(h 5) (resp. O(h 6)). We also compare the obtained formulae with projection methods.
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Research supported by AI MA/08/182 and URAC-05.
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Allouch, C., Sablonnière, P. & Sbibih, D. Solving Fredholm integral equations by approximating kernels by spline quasi-interpolants. Numer Algor 56, 437–453 (2011). https://doi.org/10.1007/s11075-010-9396-7
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DOI: https://doi.org/10.1007/s11075-010-9396-7