Ordinary Differential Equations and Integral Equations

ISBN: 9780444506009 出版年：2001 页码：559 Baker, C T H Monegato, G Berghe, G vanden North Holland_RM

Preface. Numerical methods for ordinary differential equations in the 20th century (J.C. Butcher). Initial value problems for ODE's in problem solving environments (L.F. Shampine, R.M. Corless). Resolvent conditions and bounds on the powers of matrices, with relevance to numerical stability of initial value problems (N. Borovykh, M.N. Spijker). Numerical bifurcation analysis for ODEs (W. Govaerts). Preserving algebraic invariants with Runge-Kutta methods (A. Iserles, A. Zanna). Performance of two methods for solving separable Hamiltonian systems (V. Antohe, I. Gladwell). Order stars and stiff integrators (E. Hairer, G. Wanner). Exponentially fitted Runge-Kutta methods (G. Vanden Berghe, H. De Meyer, M. Van Daele, T. Van Hecke). Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs (J.R. Cash). Software and algorithms for sensitivity analysis of large-scale differential algebraic systems (S. Li, L. Petzold). Compensating for order variation in mesh refinement for direct transcription methods (J.T. Betts, N. Biehn, S.L. Campbell, W.P. Huffman). Continuous numerical methods for ODEs with defect control (W.H. Enright). Numerical solutions of stochastic differential equations - implementations and stability issues (K. Burrage, P. Burrage, T. Mitsui). Numerical modelling in biosciences using delay differential equations (G.A. Bocharov, F.A. Rihan). Dynamics of constrained differential delay equations (J. Norbury, R.E. Wilson). A perspective on the numerical treatment of Volterra equations (C.T.H. Baker) Numerical stability of nonlinear delay differential equations of neutral type (A. Bellen, N. Guglielmi, M. Zennaro). Numerical bijurcation analysis of delay differential equations (K. Engelborghs, T. Luzyanina, D. Roose). How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation? (N.J. Ford, V. Wulf). Designing efficient software for solving delay differential equations (C.A.H. Paul). Introduction to the numerical analysis of stochastic delay differential equations (E. Buckwar). Retarded differential equations (C.T.H. Baker). Adaptive space-time finite element solution for Volterra equations arising in viscoelasticity problems (S. Shaw, J.R. Whiteman). CP methods for the Schrodinger equation (L.Gr. Ixaru). Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions (A.L. Andrew). Numerical methods for higher order Sturm-Liouville problems (L. Greenberg, M. Marletta). On a comuter assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm-Liouville problem (B.M. Brown, D.K.R. McCormack, A. Zettl). Numerical analysis for non-dimensional Cauchy singular integral equations (P. Junghanns, B. Silbermann). Numerical methods for integral equations of Mellin type (J. Elschner, I.G. Graham). Quadrature methods for 2D and 3D problems (A. Rathsfeld). Qualocation (I.H. Sloan). A sparse H-matrix arithmetic: general complexity estimates (W. Hackbusch, B.N. Khoromskij) Multilevel methods for the h-, p-, and hp-versions of the boundary element method (E.P. Stephan). Domain decomposition methods via boundary integral equations (G.C. Hsiao, O. Steinback, W.L. Wendland). Author Index Volume 125.