Geodesic
A numerical solution of one class of Volterra integral equations of the first kind in terms of the machine arithmetic features
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 3, pp. 119-129

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The research is devoted to a numerical solution of the Volterra equations of the first kind that were obtained using the Laplace integral transforms for solving the equation of heat conduction. The paper consists of an introduction and two sections. The first section deals with the calculation of kernels from the respective integral equations at a fixed length of the significand in the floating point representation of a real number. The PASCAL language was used to develop the software for the calculation of kernels, which implements the function of tracking the valid digits of the significand. The test examples illustrate the typical cases of systematic error accumulation. The second section presents the results obtained from the computational algorithms which are based on the product integration method and the midpoint rule. The results of test calculations are presented to demonstrate the performance of the difference methods.
Keywords: Volterra integral equations of the first kind; numerical solution; product integration method. 
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     author = {S. V. Solodusha and I. V. Mokry},
     title = {A numerical solution of one class of {Volterra} integral equations of the first kind in terms of the machine arithmetic features},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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S. V. Solodusha; I. V. Mokry. A numerical solution of one class of Volterra integral equations of the first kind in terms of the machine arithmetic features. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 3, pp. 119-129. http://geodesic.mathdoc.fr/item/VYURU_2016_9_3_a9/