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International Journal for Computational Methods in Engineering Science and Mechanics Volume 20, 2019 - Issue 5: Special issue on Nonlinear Differential Equations- Theory, Modeling and Computations; Guest editor: Ritesh Kumar Dubey
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Articles

A fourth-order orthogonal spline collocation method to fourth-order boundary value problems

Bhal Santosh KumarDepartment of Mathematics, BITS Pilani K K Birla Goa Campus, Zuarinagar, Goa, IndiaView further author information
,
P. DanumjayaDepartment of Mathematics, BITS Pilani K K Birla Goa Campus, Zuarinagar, Goa, IndiaCorrespondence[email protected]
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&
Anil KumarDepartment of Mathematics, BITS Pilani K K Birla Goa Campus, Zuarinagar, Goa, IndiaView further author information
Pages 460-470 | Published online: 22 Apr 2019

References

  • R. P. Agarwal, Boundary Value Problems for Higher Order Differential Equations, Singapore, India: World Scientific, 1986.
  • L. A. Peletier, W. C. Troy, and R. C. A. M. Van der Vorst, “Stationary solutions of a fourth-order nonlinear diffusion equation,” Differ. Equ., vol. 31, no. 2, pp. 301–314, 1995.
  • J. Rashidinia, “Finite difference methods for a class of two point boundary value problems,” IUST Int. J. Engrg. Sci., vol. 19, no. 5–2, pp. 67–72, 2008.
  • M. E. Gamel and A. I. Zayed, “Sinc-Galerkin method for solving nonlinear boundary value problems,” Comput. Math. Appl., vol. 48, no. 9, pp. 1285–1298, 2004. DOI: 10.1016/j.camwa.2004.10.021.
  • D. J. Fyfe, “The use of cubic splines in the solution of certain fourth order boundary value problems,” Comput. J., vol. 13, no. 2, pp. 204–205, 1970. DOI: 10.1093/comjnl/13.2.204.
  • N. Papamichael and A. J. Worsey, “A cubic spline method for the solution of a linear fourth-order two-point boundary value problem,” J. Comput. Appl. Math., vol. 7, no. 3, pp. 187–189, 1981. DOI: 10.1016/0771-050X(81)90017-6.
  • M. Sakai and R. Usmani, “Spline solutions for nonlinear fourth order two point boundary value problems,” Publ. Res. Inst. Math. Sci. Kyoto Univ., vol. 19, no. 1, pp. 135–144, 1983. DOI: 10.2977/prims/1195182980.
  • U. Ascher, S. Pruess, and R. D. Russell, “On spline basis selection for solving differential equations,” SIAM J. Numer. Anal., vol. 20, no. 1, pp. 121–142, 1983. DOI: 10.1137/0720009.
  • J. B. Swift and P. C. Hohenberg, “Hydrodynamic fluctuations at the convective instability,” Phys. Rev. A, vol. 15, no. 1, pp. 319–328, 1977. DOI: 10.1103/PhysRevA.15.319.
  • L. A. Peletier and V. Rottschafer, “Pattern selection of solutions of the Swift-Hohenberg equation,” Phys. D, vol. 194, no. 1–2, pp. 95–126, 2004. DOI: 10.1016/j.physd.2004.01.043.
  • P. C. Hohenberg and J. B. Swift, “Effects of additive noise at the onset of Rayleigh-Bénard convection,” Phys. Rev. A, vol. 46, no. 8, pp. 47–73–4785, 1992. DOI: 10.1103/PhysRevA.46.4773.
  • Y. Pomeau and P. Manneville, “Wave length selection in cellular flows,” Phys. Lett. A, vol. 75, no. 4, pp. 296–298, 1980. DOI: 10.1016/0375-9601(80)90568-X.
  • J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett., vol. 73, no. 22, pp. 2978–2981, 1994. DOI: 10.1103/PhysRevLett.73.2978.
  • I. H. Sloan, D. Tran, and G. Fairweather, “A fourth-order cubic spline method for linear second-order two-point boundary value problems,” IMA J. Numer. Anal., vol. 13, no. 4, pp. 591–607, 1993. DOI: 10.1093/imanum/13.4.591.

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