Numerical Methods for Evolutionary Equations with Delay and Software Package PDDE

  • Vladimir Pimenov
  • Andrey Lozhnikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


The paper gives a survey of the author’s results on the grid-based numerical algorithms for solving the evolutionary equations (parabolic and hyperbolic) with the effect of heredity on a time variable. From uniform positions we construct analogs of schemes with weights for the one-dimensional heat conduction equation with delay of general form, analog of a method of variable directions for the equation of parabolic type with time delay and two spatial variables, analog of the scheme with weights for the equation of hyperbolic type with delay. For the one-dimensional heat conduction equation and the wave equation we obtained conditions on the weight coefficients that ensure stability on the prehistory of the initial function. Numerical algorithms are implemented in the form of software package Partial Delay Differential Equations (PDDE) toolbox.


grid-based numerical methods delay partial differential equations stability convergence order software package 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vladimir Pimenov
    • 1
  • Andrey Lozhnikov
    • 1
    • 2
  1. 1.Ural Federal UniversityEkaterinburgRussia
  2. 2.Institute of Mathematics and MechanicsEkaterinburgRussia

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