Numerical solution of boundary value problems in ordinary differential equations

By R. Usmani. 1967

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Citations in the corpus

Invertible Residual Networks (2018, background): “Yet, the applicability of such an approach to non-linear, time-dependent dynamics is unclear as they only refer to kinematic eigenvalues [5] which generalize the theory of linear time-invariant ODEs to some subclassses (e.g. diagonally dominant matrices, Example 3.7 in [5]) of time-dependent ODEs.”
GYRE: An open-source stellar oscillation code based on a new Magnus Multiple Shooting Scheme (2013, background): “Ascher et al. (1995) discuss it in considerable depth; here, we highlight the important aspects.”
Domain Decomposition Methods in Optimal Control of Partial Differential Equations (2004, methodology): “We may use the methods of Asher, Matheij and Russell [3] in order to solve (2.”
A BVP solver based on residual control and the Maltab PSE (2001, methodology): “The formula is viewed as a mono-implicit method in Cash [1983] and implemented in HAGRON [Cash 1988].”
( Preprint ) AAS 09-334 A SURVEY OF NUMERICAL METHODS FOR OPTIMAL CONTROL (2009, background): “Equation (29) together with the isolation property leads to the fact that ck = x(τk) The use of orthogonal collocation to solve differential equ ations was originally introduced in Ref.”
Solving ODEs with MATLAB (2003, methodology): “When applied to first-order systems, the solvers COLSYS (Ascher, Christiansen, & Russell 1979, 1981) and COLNEW (Ascher et al. 1995; Bader & Ascher 1987) can be viewed as implementing the family of”
Incorporating a class of constraints into the dynamics of optimal control problems (2009, background): “These higher-order representations in 1 and ,r result in fewer unknowns in the collocation scheme and lead to a higher accuracy of the numerical solution [18, 20].”
Numerical Solution of Ordinary Differential Equations: Atkinson/Numerical (2009, methodology): “For a comprehensive introduction to this and to the general subject of the numerical solution of two-point boun dary value problems, see Keller [53], Ascher et al [9], or Ascher and Petzold [10, Chap .”
Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, methodology): “In fact, this latter example gives rise to the name shooting method for another approach to solving 2-point BVPs that is discussed in [4] and [54], for example.”