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Titlebook: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan; Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Bo

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https://doi.org/10.1007/978-3-663-20267-7oints according to a smooth homotopy function and the accuracy is superior to other EFMs. The basic algorithm is presented in the absence of stationary points but we extend it to cater for highly oscillatory integrals with stationary points. The presentation is accompanied by numerical experiments which demonstrate the power of our approach.
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Numerical Analysis and Computational Solution of Integro-Differential Equations,non-standard integro-differential equations type that arise as mathematical models in applications. We shall see that in addition to numerous open problems in the numerical analysis of such equations, many challenges in the computational solution of non-standard Volterra and Fredholm integro-differential equations are waiting to be addressed.
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An Adaptive Filon Algorithm for Highly Oscillatory Integrals,oints according to a smooth homotopy function and the accuracy is superior to other EFMs. The basic algorithm is presented in the absence of stationary points but we extend it to cater for highly oscillatory integrals with stationary points. The presentation is accompanied by numerical experiments which demonstrate the power of our approach.
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On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics,en problems, and in particular explain the recently established connection between the distribution of pair correlations of sequences on the torus and certain concepts from additive combinatorics. Furthermore, we slightly improve a result recently given by Jean Bourgain in Aistleitner et al. (Isr. J. Math., to appear. Available at .).
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