Computing continuous-time growth models with boundary conditions via wavelets

Journal of Economic Dynamics and Control

Volumn 31, Issue 11, 2007, Pages 3614-3643

  Esteban Bravo, Mercedes ^a   Vidal Sanz, Jose M ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Boundary value problems; Continuous time growth models; Wavelets

Indexed keywords

EID: 34548480935     PISSN: 01651889     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jedc.2007.01.012     Document Type: Article

References (33)

1. Ascher, U.M., Mattheij, M.M., Russell, R.D., 1995. Numerical solution of boundary value problems for ordinary differential equations. Classics in Applied Mathematics, vol. 13. Society for Industrial and Applied Mathematics, Philadelphia.
2. Battle G. A block spin construction of ondelettes. Commun. Math. Phys. 110 (1987) 601-615
3. Beylkin G. On the representation of operators in basis of compactly supported wavelets. SIAM J. Numer. Anal. 6 (1992) 1716-1740
4. Beylkin, G., 1993. Wavelets and fast numerical algorithms. In: Different perspectives on wavelets. Proceedings of Symposia in Applied Mathematics, vol. 47. American Mathematical Society, RI.
5. de Boor C., and Schwartz B. Collocation at Gaussian points. SIAM J. Numer. Anal. 10 (1973) 582-606
6. Chui, C.K. (Ed.), 1992. Wavelets. A tutorial in Theory and Applications. Academic Press, Boston, MA.
7. Conte S.D. The numerical solution of linear boundary value problems. SIAM Rev. 8 (1966) 309-321
8. Daubechies, I., 1992. Ten Lectures on Wavelets. (2nd printing with corrections) CBMS-NFS Series in Applied Mathematics. SIAM, Philadelphia, PA.
9. Daubechies I. Two Recent Results on Wavelets. In: Schumaker L.L., and Webb G. (Eds). Recent Advances in Wavelet Analysis, Wavelet Analysis and its Applications vol. 3 (1994), Academic Press, Boston, MA 237-257
10. Esteban-Bravo M. Computing equilibria in general equilibrium models via interior-point method. Computational Economics 23 2 (2004) 147-171
11. Goffe W.L. A user's guide to the numerical solution of two-point boundary value problems arising in continuous time dynamic economic models. Computational Economics 6 3-4 (1993) 249-255
12. Haar A. Zur Theorie der orthogonalen Funktionen-Systeme. Math. Ann. 69 (1910) 331-371
13. Judd K.L. Numerical Methods in Economics (1998), The MIT Press, Cambridge, MA
14. Keller H.B. Numerical Methods for Two Point Boundary Value Problems (1968), Ginn-Blaisdell, Waltham, MA
15. Keller H.B. Numerical Methods for Two Point Boundary Value Problems. CBMS-NSF Regional Conference Series in Applied Mathematics (1976), Capital City Press, Montpelier, Vermont
16. Latto A., Resnikoff H.L., and Tenenbaum E. The evaluation of connection coefficients of compactly supported wavelets. In: Maday Y. (Ed). Proceedings of the French-USA Workshop on Wavelets and Turbulence (1991), Princeton University, Springer, New York
17. Lemarié P.G. Ondelettes a localisation exponentielle. J. Math. Pures Appl. 67 (1988) 227-236
18. Lucas T.R., and Reddien G.W. Some collocation methods for nonlinear boundary value problems. SIAM J. Numer. Anal. 9 (1972) 341-356
19. Mallat S. A theory of multiresolution signal decomposition, the wavelet representation. IEE Trans. Pattern Anal. Machine Intell. 11 (1989) 674-693
20. Marimon, R., Scott, A. (Eds.), 1999. Computational Methods for the Study of Dynamics Economics. Oxford University Press, Oxford.
21. Meyer, Y., 1992. Wavelets and Operators. Cambridge University Press, Cambridge, UK. (English translation from French, Ondelettes et opérateurs, vols. I and II, 1990, Hermann, Paris).
22. Meyer Y. Wavelets: Algorithms and Applications (1993), SIAM, Philadelphia, PA
23. Osborne M.R. On shooting methods for boundary value problems. J. Math. Anal. Appl. 27 (1969) 417-433
24. Prenter P.M. Splines and Variational Methods (1975), Wiley, New York
25. Roberts, S.M., Shipman, J.S., 1972. Two-point boundary value problems: shooting methods. Modern analytic and computational methods in science and mathematics, vol. 31. American Elsevier, New York.
26. Russell R.D., and Shampine L.F. A collocation method for boundary value problems. Numer. Math. 19 (1972) 1-28
27. Rust J. Numerical Dynamic Programming in Economics. In: Amman H.M., Kendrick D.A., and Rust J. (Eds). Handbook of Computational Economics vol. I (1996), Elsevier Science, Amsterdam
28. Santos M. Numerical solution of dynamic economic models. In: Taylor J.B., and Woodford M. (Eds). Handbook of Macroeconomics vol. I (1999), Elsevier Science, Amsterdam
29. Thomée, V., 1973. Convergence estimates for semi-discrete Galerkin methods for initial value problems. Lecture Notes in Mathematics, vol. 333, pp. 243-262
30. Vainikko G.M. Galerkin's perturbation method and the general theory of approximate methods for nonlinear equations. U.S.S.R. Comput. Math. and Math. Phys. 7 (1967) 1-41
31. Varga R.S. Functional Analysis and Approximation Theory in Numerical Analysis. Regional Conference Series in Applied Mathematics vol. 3 (1971), SIAM, Philadelphia, PA
32. Venkatesh P.K. On the optimum control of differential-algebraic equations. J. Optim. Theory Appl. 109 (2001) 675-689
33. Walnut D.F. An Introduction to Wavelets Analysis (2001), Birkhauser, Boston