760
Views
1
CrossRef citations to date
0
Altmetric
Research Articles

Tension spline method for the solution of elliptic equations

& ORCID Icon
Pages 604-610 | Received 16 Jun 2017, Accepted 14 Apr 2019, Published online: 09 May 2019

References

  • Barkeshli K. Advanced electromagnetics and scattering theory. New York: Springer; 2015.
  • Datta S. Quantum transport: atom to transistor. London: Cambridge University Press; 2005.
  • Borden B. Radar imaging of airborne targets. New York: Taylor & Francis; 1999.
  • Tian Z. An high order compact finite difference scheme for the second dimensional Poisson equation. J Northwest Univ. 1996;26(2):109–114.
  • Zhang J. Multigrid method and fourth order compact scheme for 2d Poisson equation with unequal meshsize discretization. J Comput Phys. 2002;179:170–179. doi: 10.1006/jcph.2002.7049
  • Zapata RIMU. High-order implicit finite difference schemes for the two-dimensional Poisson equation. Appl Math Comput. 2017;309:222–244.
  • Wang Y, Zhang J. Sixth order compact scheme combined with multigrid method and extrapolation technique for 2d Poisson equation. J Comput Phys. 2009;228:137–146. doi: 10.1016/j.jcp.2008.09.002
  • Singer I, Turkel E. High-order finite difference methods for the Helmholtz equation. Comput Method Appl Math. 1998;163:343–358.
  • Fu Y. Compact fourth order finite difference schemes for Helmholtz equation with high wave numbers. J Comput Math. 2008;26:98–111.
  • Romenski V. The method of spline collocation for the Poisson equation. J Comput Acoust. 1979;81:81–86.
  • Bialecki B. Superconvergence of orthogonal spline collocation in the solution of Poisson's equation. Numer Methods Partial Diff Eqn. 1999;15:285–303. doi: 10.1002/(SICI)1098-2426(199905)15:3<285::AID-NUM2>3.0.CO;2-1
  • Christara CC. Quadratic spline collocation methods for elliptic partial differential equations. BIT. 1994;34:33–61. doi: 10.1007/BF01935015
  • Houstis E, Vavalis E, Rice J. Convergence of o(h4) cubic spline collocation methods for elliptic partial differential equations. SIAM J Numer Anal. 1988;25(1):54–74. doi: 10.1137/0725006
  • Fairweather G, Karageorghis A, Maack J. Compact optimal quadratic spline collocation methods for the Helm-holtz equation. J Comput Phys. 2011;230:2880–2895. doi: 10.1016/j.jcp.2010.12.041
  • Rashidinia J, Mohammadi R, Ghasemi M. Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives. Appl Math Comput. 2007;190:1762–1766.
  • Rashidinia J, Mohammadi R, Jalilian R. Spline solution of nonlinear singular boundary value problems. Int J Comput Math. 2008;85:39–52. doi:10.1080/00207160701293048
  • Khan I, Aziz T. Tension spline method for second-order singularly perturbed boundary-value problems. Int J Comput Math. 2005;82(12):1547–1553. doi:10.1080/00207160410001684280
  • Aghamohamadi M, Rashidinia J, Ezzati R. Tension spline method for solution of non-linear Fisher equation. Appl Math Comput. 2014;249:399–407.
  • Rashidinia J, Mohammadi R. Tension spline solution of nonlinear sine-Gordon equation. Numer Algor. 2011;56:129–142. doi:10.1007/s11075-010-9377-x
  • Mohanty R, Dey S. A new finite difference discretization of order four for (∂u/∂n) for two dimensional quasi-linear elliptic boundary value problems. Int J Comput Math. 2001;76:505–516. doi: 10.1080/00207160108805043
  • Mohanty R, Jain MK, Dhall D. High accuracy cubic spline approximation for two dimensional quassi-linear elliptic boundary value problems. Int J Comput Math. 2013;37:155–171.
  • Yaw K, Kossi E. Higher-order accurate finite volume discretization of Helmholtz equations with pollution effects reductions. Int J Innov Edu Res. 2018;6(2):130–148.
  • Ghimire BK, Tian HY, Lamichhane A. Numerical solutions of elliptic partial differential equations using Chebyshev polynomials. Comput Math Appl. 2016;72:1042–1054. doi: 10.1016/j.camwa.2016.06.012
  • Dangal T, Chena C, Lin J. Polynomial particular solutions for solving elliptic partial differential equations. Comput Math Appl. 2017;73:60–70. doi: 10.1016/j.camwa.2016.10.024
  • Shiralashetti S, Kantli M, Deshi AB. A new wavelet multigrid method for the numerical solution of elliptic type differential equations. Alex Eng J. 2018;57(1):203–209. doi:10.1016/j.aej.2016.12.007