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.

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  1. Shevchenko, Pavel V.; Luo, Xiaolin: Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rate (2017)
  2. Schmaltz, Christian; Peter, Pascal; Mainberger, Markus; Ebel, Franziska; Weickert, Joachim; Bruhn, Andrés: Understanding, optimising, and extending data compression with anisotropic diffusion (2014) ioport
  3. Soliman, A.A.: Numerical simulation of the FitzHugh-Nagumo equations (2012)
  4. Randrianalisoa, Jaona; Dendievel, Remy; Bréchet, Yves: Ablative degradation of cryogenic thermal protection and fuel boil-off: improvement of using graded density insulators (2011)
  5. Bae, Egil; Weickert, Joachim: Partial differential equations for interpolation and compression of surfaces (2010)
  6. Harley, C.: Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation (2010)
  7. Jabbarzadeh, Ehsan; Abrams, Cameron F.: Simulations of chemotaxis and random motility in 2D random porous domains (2007)
  8. Esen, A.; Kutluay, S.: A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. (2004)
  9. Otaka, Masaaki; Yoshida, Toshihiro: Study on option pricing in an incomplete market with stochastic volatility based on risk premium analysis (2003)
  10. Li, Haitao: Pricing of swaps with default risk (1998)
  11. van der Houwen, P.J.; Sommeijer, B.P.: Splitting methods for three-dimensional transport models with interaction terms (1997)
  12. Verwer, J.G.; Sommeijer, B.P.: Stability analysis of an odd-even-line hopscotch method for three-dimensional advection-diffusion problems (1997)
  13. Sommeijer, B.P.; Kok, J.: Splitting methods for three-dimensional bio-chemical transport (1996)
  14. Sommeijer, B.P.; van der Houwen, P.J.; Kok, J.: Time integration of three-dimensional numerical transport models (1994)
  15. Srinivas, K.; Fletcher, C.A.J.: Computational techniques for fluid dynamics. A solutions manual (1992)
  16. Luchini, Paolo: A deferred-correction multigrid algorithm based on a new smoother for the Navier-Stokes equations (1991)
  17. Hundsdorfer, W.H.; Verwer, J.G.: Linear stability of the hopscotch scheme (1989)
  18. Sleijpen, G.L.G.: Strong stability results for the hopscotch method with applications to bending beam equations (1989)
  19. Ten Thije Boonkkamp, J.H.M.: The odd-even hopscotch pressure correction scheme for the incompressible Navier-Stokes equations (1987)
  20. 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)

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