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Galerkin methods with splines for singular integral equations over (0,1). (English) Zbl 0549.65093

Author’s summary: A convergence analysis of Galerkin methods with splines for strongly elliptic singular integral equations over the interval (0,1) is given. As trial functions we utilize smoothest polynomial splines on arbitrary meshes and continuous splines on special nonuniform partitions, multiplied by a weight function. Using inequalities of Gårding type for singular integral operators in weighted \(L^ 2\) spaces and the complete asymptotics of solutions at the endpoints, we provide error estimates in certain Sobolev norms.
Reviewer: M.Schleiff

MSC:

65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
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References:

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