Hopscotch

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 39 articles )

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  1. Schmaltz, Christian; Peter, Pascal; Mainberger, Markus; Ebel, Franziska; Weickert, Joachim; Bruhn, Andrés: Understanding, optimising, and extending data compression with anisotropic diffusion (2014)
  2. Soliman, A.A.: Numerical simulation of the FitzHugh-Nagumo equations (2012)
  3. Randrianalisoa, Jaona; Dendievel, Remy; Bréchet, Yves: Ablative degradation of cryogenic thermal protection and fuel boil-off: improvement of using graded density insulators (2011)
  4. Bae, Egil; Weickert, Joachim: Partial differential equations for interpolation and compression of surfaces (2010)
  5. Harley, C.: Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation (2010)
  6. Jabbarzadeh, Ehsan; Abrams, Cameron F.: Simulations of chemotaxis and random motility in 2D random porous domains (2007)
  7. Esen, A.; Kutluay, S.: A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. (2004)
  8. Otaka, Masaaki; Yoshida, Toshihiro: Study on option pricing in an incomplete market with stochastic volatility based on risk premium analysis (2003)
  9. Li, Haitao: Pricing of swaps with default risk (1998)
  10. van der Houwen, P.J.; Sommeijer, B.P.: Splitting methods for three-dimensional transport models with interaction terms (1997)
  11. Verwer, J.G.; Sommeijer, B.P.: Stability analysis of an odd-even-line hopscotch method for three-dimensional advection-diffusion problems (1997)
  12. Sommeijer, B.P.; Kok, J.: Splitting methods for three-dimensional bio-chemical transport (1996)
  13. Sommeijer, B.P.; van der Houwen, P.J.; Kok, J.: Time integration of three-dimensional numerical transport models (1994)
  14. Srinivas, K.; Fletcher, C.A.J.: Computational techniques for fluid dynamics. A solutions manual (1992)
  15. Luchini, Paolo: A deferred-correction multigrid algorithm based on a new smoother for the Navier-Stokes equations (1991)
  16. Hundsdorfer, W.H.; Verwer, J.G.: Linear stability of the hopscotch scheme (1989)
  17. Sleijpen, G.L.G.: Strong stability results for the hopscotch method with applications to bending beam equations (1989)
  18. Ten Thije Boonkkamp, J.H.M.: The odd-even hopscotch pressure correction scheme for the incompressible Navier-Stokes equations (1987)
  19. ten Thije Boonkkamp, J.H.M.; Verwer, J.G.: On the odd-even hopscotch scheme for the numerical integration of time- dependent partial differential equations (1987)
  20. ter Maten, E.Jan W.; Sleijpen, Gerard L.G.: A convergence analysis of hopscotch methods for fourth order parabolic equations (1986)

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