Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methods. (English) Zbl 0998.65131
Authors’ abstract: The numerical solution of a Volterra integral equation with a certain weakly singular kernel, depending on a real parameter \(\mu\) is considered. Although for certain values of \(\mu\) this equation possesses an infinite set of solutions, we are able to prove that Euler’s method converges to a particular solution. It is also shown that the error allows an asymptotic expansion in fractional powers of the stepsize, so that general extrapolation algorithms, like the E-algorithm, can be applied to improve the numerical results. This is illustrated by means of some examples.
Reviewer: E.Deeba (Houston)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
Keywords:
convergence; error bounds; numerical examples; Volterra integral equation; weakly singular kernel; Euler’s method; algorithms; E-algorithmReferences:
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