TY - BOOK ID - 80819492 TI - Collocation methods for Volterra integral and related functional differential equations PY - 2004 SN - 9780511543234 9780521806152 9780511265884 0511265883 0511263619 9780511263613 0511265166 9780511265167 0511543239 0521806151 1107158818 1280749911 9786610749911 0511317557 0511264429 9781107158818 9781280749919 6610749914 9780511317552 9780511264429 PB - Cambridge, UK ; New York : Cambridge University Press, DB - UniCat KW - Collocation methods KW - Volterra equations KW - 519.64 KW - 681.3*G19 KW - Numerical analysis KW - Differential equations KW - Integral equations KW - 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) KW - Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) KW - 519.64 Numerical methods for solution of integral equations. Quadrature formulae KW - Numerical methods for solution of integral equations. Quadrature formulae KW - Numerical solutions KW - Collocation methods. KW - Numerical solutions. UR - https://www.unicat.be/uniCat?func=search&query=sysid:80819492 AB - 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. ER -