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This paper is concerned with the numerical approximation of definite integrals over [—1, 1], in which the function /to be integrated has isolated singularities near [ —1, 1 ]. Complex variable techniques are used to study the effectiveness of the method of subtracting out complex singularities.
In this paper, two-dimensional cubature error bounds are developed. It is assumed that the function to be integrated is analytic, and that the domain of integration is contained in [—1, 1] X [—1, 1]. Tables of error constants for several cubature rules and domains of integration are included.
1. Introduction. One of the objections to the use of a one-step method to integrate a system of ordinary differential equations is that an estimate of the accumulated truncation error is difficult to make. If an attempt is made at appraising the truncation error, it is usually confined to an approximate evaluation of the local truncation error. A scheme for… (More)