Numerical Methods for Ordinary Differential Equations: Proceedings of the Workshop held in L'Aquila (Italy), September 16-18, 1987
Alfredo Bellen, Charles W. Gear, Elvira Russo
Springer, Sep 5, 1989 - Mathematics - 136 pages
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
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Stability in Linear Abstract Differential Equations pag
Parallelism Across the Steps for Difference and Differential
DAEs ODEs with Constraints and Invariants
3 other sections not shown
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A-stable algebraic Analysis applied approximation bound Chebyshev acceleration Chebyshev-accelerated Jacobi collocation consider criterion defined denotes diagonal digraph dominant eigenvalue dominant eigenvectors Edited eigenvalues eigenvector EPUS evaluations example explicit extrapolation families of matrices formula function iteration function iteration methods given global error implementation implicit initial value problem integration invariants iteration error iteration function iteration method Jacobi method Jacobian matrix linear Mathematics model problem N0rsett nonlinear norm number of iterations Numerical Methods numerical solution obtained ODEs ordinary differential equations parallel algorithm parallel computation Pj un+j polynomial problem 2.3 Proceedings processors Proof rate of convergence reduced relaxation parameters residue smoothing RK-methods Runge-Kutta methods satisfy semi-explicit form Seminar sequential smoothed Jacobi iteration smoothed SSOR smoothing matrix solve spectral radius spectrum stability step Table Theorem Theory tolerance variables vector y(xn yn+1 zero