124
Views
2
CrossRef citations to date
0
Altmetric
Articles

Numerical approximations of second-order matrix differential equations using higher degree splines

, , &
Pages 472-489 | Received 31 Jan 2013, Accepted 28 Aug 2013, Published online: 14 Feb 2014

References

  • Loscalzo FR, Talbot TD. Spline function approximations for solutions of ordinary differential equations. SIAM J. Numer. Anal. 1967;4:433–445.
  • Al-Said EA. The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Comput. Math. Appl. 2001;42:861–869.
  • Al-Said EA, Noor MA. Cubic splines method for a system of third-order boundary value problems. Appl. Math. Comput. 2003;142:195–204.
  • Kadalbajoo MK, Patidar KC. Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. Appl. Math. Comput. 2002;131:299–320.
  • Micula G, Revnic A. An implicit numerical spline method for systems for ode’s. Appl. Math. Comput. 2000;111:121–132.
  • Defez E, Soler L, Hervás A, Santamaría C. Numerical solutions of matrix differential models using cubic matrix splines. Comput. Math. Appl. 2005;50:693–699.
  • Defez E, Soler L, Hervás A, Tung MM. Numerical solutions of matrix differential models using cubic matrix splines II. Math. Comput. Model. 2007;46:657–669.
  • Ascher U, Pruess S, Russell RD. On spline basis selection for solving differential equations. SIAM J. Numer. Anal. 1983;20:121–142.
  • Brunner H. On the divergence of collocation solutions in smooth piecewise polynomial spaces for volterra integral equations. BIT Numer. Math. 2004;44:631–650.
  • Micula G. Approximate solutions of the differential equation yʺ = f (x, y) with spline functions. Math. Comp. 1973;27:807–816.
  • Tung MM, Defez E, Sastre J. Numerical solutions of second-order matrix models using cubic-matrix splines. Comput. Math. Appl. 2008;56:2561–2571.
  • Defez E, Tung MM, Ibáñez J, Sastre J. Approximating and computing nonlinear matrix differential models. Math. Comput. Model. 2012;55:2012–2022.
  • Golub GH, Van Loan CF. Matrix computations. 2nd ed. Baltimore (MD): The Johns Hopkins University Press; 1989.
  • Graham A. Kronecker products and matrix calculus with applications. New York (NY): Wiley; 1981.
  • Claeyssen JR, Canahualpa G, Jung C. A direct approach to second-order matrix non-classical vibrating equations. Appl. Numer. Math. 1999;30:65–78.
  • Froese C. Numerical solutions of the hartree-fock equations. Can. J. Phys. 1963;41:1895–1910.
  • Marzulli P. Global error estimates for the standard parallel shooting method. J. Comput. Appl. Math. 1991;34:233–241.
  • Ortega JM. Numerical analysis: a second course. New York (NY): Academic Press; 1972.
  • Shore BW. Comparison of matrix methods to the radii schrödinger eigenvalue equation: the morse potential. J. Chem. Phys. 1971;59:6450–6463.
  • Zhang JF. Optimal control for mechanical vibration systems based on second-order matrix equations. Mech. Syst. Signal Pr. 2002;16:61–67.
  • Flett TM. Differential analysis. Cambridge, MA: Cambridge University Press; 1980.
  • Ibáñez J. MatLab implementation for matrix splines (MIMS). Available from: http://personales.upv.es/jjibanez/MIMS.html
  • Hairer E, Nørsett SP, Wanner G. Solving ordinary differential equations I: nonstiff problems. 2008. Available from: http://www.bibsonomy.org/bibtex/26bfd1a0356243229b8d30cb296e19f48/brouder.
  • Tung MM, Soler L, Defez E, Hervás A. Cubic-matrix splines and second-order matrix model. In: The 14th European Conference on Mathematics for Industry (ECMI 2006); Spain: Springer, Universidad Carlos III de Madrid; 2006.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.