Hopscotch: a fast second order partial differential equations solver. An idea of Gordon for the numerical solution of evolutionary problems is reformulated and shown to be equivalent to a Peaceman-Rachford process. A fast computational process is then developed and applied to parabolic and elliptic problems, both linear and non-linear. This algorithm is very efficient with regard to computing time, storage requirements and ease of programming. Several fairly general conditions are given which ensure convergence for parabolic and elliptic problems.

References in zbMATH (referenced in 45 articles )

Showing results 1 to 20 of 45.
Sorted by year (citations)

1 2 3 next

  1. Wu, Dan; Lv, Junliang; Qian, Hao: Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes (2022)
  2. Chapwanya, M.; Jejeniwa, O. A.; Appadu, A. R.; Lubuma, J. M.-S.: An explicit nonstandard finite difference scheme for the FitzHugh-Nagumo equations (2019)
  3. Shevchenko, Pavel V.; Luo, Xiaolin: Valuation of variable annuities with guaranteed minimum withdrawal benefit under stochastic interest rate (2017)
  4. Schmaltz, Christian; Peter, Pascal; Mainberger, Markus; Ebel, Franziska; Weickert, Joachim; Bruhn, Andrés: Understanding, optimising, and extending data compression with anisotropic diffusion (2014) ioport
  5. Soliman, A. A.: Numerical simulation of the FitzHugh-Nagumo equations (2012)
  6. Randrianalisoa, Jaona; Dendievel, Remy; Bréchet, Yves: Ablative degradation of cryogenic thermal protection and fuel boil-off: improvement of using graded density insulators (2011)
  7. Bae, Egil; Weickert, Joachim: Partial differential equations for interpolation and compression of surfaces (2010)
  8. Harley, C.: Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation (2010)
  9. Jabbarzadeh, Ehsan; Abrams, Cameron F.: Simulations of chemotaxis and random motility in 2D random porous domains (2007)
  10. Esen, A.; Kutluay, S.: A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. (2004)
  11. Otaka, Masaaki; Yoshida, Toshihiro: Study on option pricing in an incomplete market with stochastic volatility based on risk premium analysis (2003)
  12. Li, Haitao: Pricing of swaps with default risk (1998)
  13. van der Houwen, P. J.; Sommeijer, B. P.: Splitting methods for three-dimensional transport models with interaction terms (1997)
  14. Verwer, J. G.; Sommeijer, B. P.: Stability analysis of an odd-even-line hopscotch method for three-dimensional advection-diffusion problems (1997)
  15. Sommeijer, B. P.; Kok, J.: Splitting methods for three-dimensional bio-chemical transport (1996)
  16. Sommeijer, B. P.; van der Houwen, P. J.; Kok, J.: Time integration of three-dimensional numerical transport models (1994)
  17. Bhattacharya, M. C.: Improved finite-difference solutions of the diffusion equation for heat conduction (1993)
  18. Srinivas, K.; Fletcher, C. A. J.: Computational techniques for fluid dynamics. A solutions manual (1992)
  19. Luchini, Paolo: A deferred-correction multigrid algorithm based on a new smoother for the Navier-Stokes equations (1991)
  20. Hundsdorfer, W. H.; Verwer, J. G.: Linear stability of the hopscotch scheme (1989)

1 2 3 next