Type I operators and the approximation of singular two-point boundary value problems |
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Authors: | Mohamed A El-Gebeily Donal O’Regan |
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Institution: | a Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia b Department of Mathematics, National University of Ireland, Galway, Ireland |
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Abstract: | A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation. |
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Keywords: | Singular differential equations Self adjoint operators Galerkin method Variational equations |
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