References for the Solution Operation Nodes and Solvers

1. P.E. Gill, W. Murray, and M.A. Saunders, User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming, Systems Optimization Laboratory (SOL), Stanford University, 2006.

2. P.E. Gill, W. Murray, and M.A. Saunders, “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization”, SIAM Review, vol. 47, no. 1, pp. 99–131, 2005.

3. P. Deuflhard, “A Modified Newton Method for the Solution of Ill-conditioned Systems of Nonlinear Equations with Application to Multiple Shooting”, Numer. Math., vol. 22, pp. 289–315, 1974.

4. A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R. Serban, D.E. Shumaker, and C.S. Woodward, “SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers”, ACM T. Math. Software, vol. 31, p. 363, 2005.

5. P.N. Brown, A.C. Hindmarsh, and L.R. Petzold, “Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems”, SIAM J. Sci. Comput., vol. 15, pp. 1467–1488, 1994.

6. P.K. Moore and L.R. Petzold, “A Stepsize Control Strategy for Stiff Systems of Ordinary Differential Equations”, Applied Numerical Mathematics, vol. 15, pp. 449–463, 1994.

7. K.E. Brenan, S.L. Campbell, and L.R. Petzold, Numerical Solutions of Initial-Value Problems in Differential-Algebraic Equations, pp. 146–147, SIAM, Philadelphia, Pa, 1996.

8. J. Demmel and others, “Error Bounds from Extra Precise Iterative Refinement,” ACM Transactions on Mathematical Software (TOMS), vol. 32, issue 2, pp. 325–351, 2006.

9. J. Chung, G.M. Hulbert, “A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-α Method”, J. Appl. Mech., vol. 60, pp. 371–375, 1993.

10. K.E. Jansen, C.H. Whiting, G.M. Hulbert, “A Generalized-α Method for Integrating the Filtered Navier–Stokes Equations with a Stabilized Finite Element Method”, Comput. Methods Appl. Mech. Engrg., vol. 190, pp. 305–319, 2000.

11. J.R. Dormand and P.J. Prince, “A family of embedded Runge-Kutta formulae”, Journal of Computational and Applied Mathematics, vol. 6 (1), pp. 19–26, 1980.

12. The ARPACK Arnoldi package, www.caam.rice.edu/software/ARPACK.

13. P. Deuflhard, “A Stepsize Control for Continuation Methods and its Special Application to Multiple Shooting Techniques”, Numer. Math., vol. 33, pp. 115–146, 1979.

14. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Teubner Verlag and J. Wiley, Stuttgart, 1996.

15. R. Rannacher, “A Feed-back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples”, East-West J. Numer. Math., vol. 4, pp. 237–264, 1996.

16. www.netlib.org/ode.

17. J. Jin, The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 2002.