×

zbMATH — the first resource for mathematics

A numerical treatment to the solution of certain first kind Fredholm integral equations. (English) Zbl 0817.65144
This paper presents results obtained by an implementation of the kernel basis method to the solution of \[ \int^ b_ a e(t) \exp[s f(t)] u(t) dt= v(s), \] \(c\leq s\leq d\), where \(v(s)\) is a given function and the range \([c, d]\) of values \(s\) does not necessarily coincide with the range of integration \([a,b]\). Test examples are used to show that the numerical solution is comparable to the exact one.
MSC:
65R20 Numerical methods for integral equations
65R30 Numerical methods for ill-posed problems for integral equations
45B05 Fredholm integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. P. Bennell, J. C. Mason,Continuous approximation methods for the regularization and smoothing of integral transforms, Rocky Mountain J. Math. 19 (1) (1989), 51–66. · Zbl 0693.65092 · doi:10.1216/RMJ-1989-19-1-51
[2] H. S. Carslaw, J. C. Jaeger,Conduction of heat in solids, (1959), Clarendon Press, Oxford. · Zbl 0029.37801
[3] W. Pogorzelski,Integral equations and their applications (1966), PWN-Pergamon Press, Warszawa. · Zbl 0137.30502
[4] G. Wahba,Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal. 14 (1977), 651–667. · Zbl 0402.65032 · doi:10.1137/0714044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.