We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the performance of the method is illustrated by some numerical examples.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 7, pp. 919–931, July, 2012.
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Katani, R., Shahmorad, S. The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals. Ukr Math J 64, 1050–1063 (2012). https://doi.org/10.1007/s11253-012-0698-x
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DOI: https://doi.org/10.1007/s11253-012-0698-x