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A quadrature method with variable step for solving linear Volterra integral equations of the second kind. (English) Zbl 1118.65132
Summary: In usual quadrature methods for solving integral equations, divide the integration interval $(a, b)$ into $n$ equal subintervals of the length $h=(b-a)/n$. In this article, we intend to divide the integration interval into n subintervals of different lengths, which solves linear Volterra integral equations more accurately than usual quadrature methods. For further information on quadrature methods with variable step see {\it L. M. Delves} and {\it J. L. Mohamed} [Computational methods for integral equations, Cambridge University Press (1985; Zbl 0592.65093)] and {\it L. M. Delves} (ed.) and {\it J. Walsh} [Numerical solution of integral equations, Oxford University Press (1974; Zbl 0294.65068)].

65R20Integral equations (numerical methods)
45D05Volterra integral equations
Full Text: DOI
[1] Atkinson, K. E.: The numerical solution of integral equations of the second kind. (1997) · Zbl 0899.65077
[2] Baker, C. T. H.; Miller, G. F.: Treatment of integral equations by numerical methods. (1982) · Zbl 0499.00015
[3] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · Zbl 0592.65093
[4] Delves, L. M.; Walsh, J.: Numerical solution of integral equations. (1974) · Zbl 0294.65068
[5] Jerri, A. J.: Introduction to integral equations with applications. (1999) · Zbl 0938.45001
[6] Kenwal, R. P.: Linear integral equations theory and technique. (1971)
[7] Kondo, J.: Integral equations. (1991) · Zbl 0743.45001
[8] Kress, R.: Linear integral equations. (1989) · Zbl 0671.45001
[9] Kyte, P. K.; Puri, P.: Computational methods for linear integral equations. (2002)