Modified Crank-Nicholson Difference Schemes for Ultra Parabolic Equations with Neumann Condition

  • Allaberen Ashyralyev
  • Serhat Yilmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


In this paper, our interest is studying the stability of difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations. For approximately solving the given problem, the second-order of accuracy modified Crank-Nicholson difference schemes are presented. Theorem on almost coercive stability of these difference schemes is established. Numerical example is given to illustrate the applicability and efficiency of our method.


Ultra parabolic equations difference schemes stability estimates matlab implementation numerical solutions 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Allaberen Ashyralyev
    • 1
    • 2
  • Serhat Yilmaz
    • 1
  1. 1.Department of MathematicsFatih UniversityIstanbulTurkey
  2. 2.Department of MathematicsITTUAshgabatTurkmenistan

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