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Collocation Methods for Volterra Integral and Related Functional Differential Equations
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  • Cited by 143
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    Liang, Hui and Brunner, Hermann 2016. On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations. BIT Numerical Mathematics,

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    Xu, Zhenhua and Xiang, Shuhuang 2016. Gauss-type quadrature for highly oscillatory integrals with algebraic singularities and applications. International Journal of Computer Mathematics, p. 1.

    Zhang, Gengen and Xiao, Aiguo 2016. Exact and numerical stability analysis of reaction-diffusion equations with distributed delays. Frontiers of Mathematics in China, Vol. 11, Issue. 1, p. 189.

    Zhao, Jingjun Cao, Yang and Xu, Yang 2016. Sinc numerical solution for pantograph Volterra delay-integro-differential equation. International Journal of Computer Mathematics, p. 1.

    Zhao, Jingjun Cao, Yang and Xu, Yang 2016. Legendre Spectral Collocation Methods for Volterra Delay-Integro-Differential Equations. Journal of Scientific Computing, Vol. 67, Issue. 3, p. 1110.

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Book description

Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.


'The clarity of the exposition, the completeness in the presentation of stated and proved theorems, and the inclusion of a long list of exercises and open problems, along with a wide and exhaustive annotated bibliography, make this monograph a useful and valuable reference book for a wide range of scientists and engineers. In particular, it can be recommended to advanced undergraduate and graduate students in mathematics and may also serve as a source of topics for MSc. and PhD. theses in this field.'

Alfredo Bellen - Universita’ di Trieste

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