Numerical solution of initial value problems in differential - algebraic equations

By M. Akanbi. 2005

1,266 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/aca690103083c23bda051cf58fcfcd5c3be43e9b

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Citations in the corpus

Solving Differential Equations in R: Package deSolve (2010, methodology): “…( t 0 ) , y ( t 0 ) , v, t 0 ) DAEs are commonly encountered in a number of scientiﬁc and engineering disciplines, e.g., in the modelling of electrical circuits or mechanical systems, in constrained variational problems, or in equilibrium chemistry (e.g., Brenan, Campbell, and Petzold 1996).”
Low rank iterative methods for projected generalized Lyapunov equations (2005, background): “Such systems arise, for instance, in spatial discretization of the instationary incompressible Stokes equation [7, 8], and the convection equation [21].”
Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts (2012, unknown): “The results on the local order of convergence obtained for implicit Runge–Kutta method [19,18] or for backward differentiation formulas [23,11] can be straightforwardly extended to complete the proof.”
Control: A perspective (2014, background): “In the 1980s there had been significant advances in numerical solution of such equations [244,110,24,278].”
Differential variational inequalities (2008, background): “A significant guide in this process is the notion of index of DAEs [9,19].”
Numerical Methods for Evolutionary Differential Equations (2008, methodology): “However, note that the constraints may have to be stabilized, the approach is less automatic, and some sparsity may be lost in the transformation as well; see [14, 34, 85].”
Control and Optimization with Differential-Algebraic Constraints (2012, background): “[9, 19, 18, 20, 29, 38] or for special DAEs arising in applications, see e.”
A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations (2006, background): “In this method, if a Lagrangian set of coordinates [17], that is, a minimal set of generalized coordinates, is chosen, locally the dynamics of the system is represented as a set of second-order ordinary differential equations (ODE), rather than the index 3 DAE introduced above.”
Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions (2006, methodology): “In this work, we can use the differential/algebraic system solver (DASSL) [5] as our ODE solver.”
Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations (2014, background): “While the qualitative theory of DAE is widely available (see [3], [19], [20]), there exist fewer results for IAE and DIDE (see, [4], [6], [7], [8], [17] and references therein).”
Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution (2002, methodology): “0 is an extension of the DASPK software [9, 10] developed by Brown, Hindmarsh, and Petzold for the solution of large-scale DAE systems.”
Adaptive Time-Stepping and Computational Stability (2006, methodology): “Thus we choose to study these phenomena and algorithms in the wellestablished and widely used ODE code Dassl, [2], and take test problems from the CWI test set, [10].”
Hybrid systems of differential-algebraic equations – Analysis and numerical solution (2009, methodology): “by a BDF method [5] or by Runge-Kutta methods [10].”
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2020, methodology): “The state is evolved using variable order and variable step size BDF methods in ixed-leading-coeicient form [12] of order q = 1, .”