Collocation Methods for Volterra Integral and Related Functional Differential Equations
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Collocation Methods for Volterra Integral and Related Functional Differential Equations: (Series Number 15 Cambridge Monographs on Applied and Computational Mathematics)

Collocation Methods for Volterra Integral and Related Functional Differential Equations: (Series Number 15 Cambridge Monographs on Applied and Computational Mathematics)


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About the Book

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.

Table of Contents:
1. The collocation method for ODEs: an introduction; 2. Volterra integral equations with smooth kernels; 3. Volterra integro-differential equations with smooth kernels; 4. Initial-value problems with non-vanishing delays; 5. Initial-value problems with proportional (vanishing) delays; 6. Volterra integral equations with weakly singular kernels; 7. VIDEs with weakly singular kernels; 8. Outlook: integral-algebraic equations and beyond; 9. Epilogue.

Review :
'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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Product Details
  • ISBN-13: 9780521806152
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 236 mm
  • No of Pages: 612
  • Returnable: N
  • Series Title: Series Number 15 Cambridge Monographs on Applied and Computational Mathematics
  • Weight: 1384 gr
  • ISBN-10: 0521806151
  • Publisher Date: 15 Nov 2004
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 40 mm
  • Width: 158 mm


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Collocation Methods for Volterra Integral and Related Functional Differential Equations: (Series Number 15 Cambridge Monographs on Applied and Computational Mathematics)
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Collocation Methods for Volterra Integral and Related Functional Differential Equations: (Series Number 15 Cambridge Monographs on Applied and Computational Mathematics)
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Collocation Methods for Volterra Integral and Related Functional Differential Equations: (Series Number 15 Cambridge Monographs on Applied and Computational Mathematics)

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