Abstract
The problem of the numerical evaluation of the integral \(I = \int\limits_a^b {f(t)dt}\) will be considered. A nonlinear technique, based on the use of Padé approximation, will be given and discussed.
The value of the integral satisfies I = y(b) , where y(x) is the solution of the initial value problem y′ = f(x) with y(a) = o. This solution is approximated using Padé approximation. Consequently a one-step method is obtained to approximate the value of I. Certain properties of this method are given, e.g. its order of convergence.
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References
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© 1976 Springer-Verlag
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Wuytack, L. (1976). The use of Pade approximation in numerical integration. In: Cabannes, H. (eds) Padé Approximants Method and Its Applications to Mechanics. Lecture Notes in Physics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015660
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DOI: https://doi.org/10.1007/BFb0015660
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