Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

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Abstract

We discuss the convergence properties of spline collocation and iterated collocation methods for a weakly singular Volterra integral equation associated with certain heat conduction problems. This work completes the previous studies of numerical methods for this type of equations with noncompact kernel. In particular, a global convergence result is obtained and it is shown that discrete superconvergence can be achieved with the iterated collocation if the exact solution belongs to some appropriate spaces. Some numerical examples illustrate the theoretical results.

MSC

65R20

Keywords

Volterra integral equation
Singular kernel
Collocation methods
Iterated collocation

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