Modified Crank-Nicholson Difference Schemes for Ultra Parabolic Equations with Neumann Condition
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.
KeywordsUltra parabolic equations difference schemes stability estimates matlab implementation numerical solutions
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- 9.Tersenov, S.A.: On boundary value problems for a class of ultraparabolic equations and their applications. Matem. Sbornik. 175, 529–544 (1987)Google Scholar
- 10.Ashyralyev, A., Yilmaz, S.: Second order of accuracy difference schemes for ultra parabolic equations. In: AIP Conference Proceedings, vol. 1389, pp. 601–604 (2011)Google Scholar
- 11.Ashyralyev, A., Yilmaz, S.: An Approximation of ultra-parabolic equations. Abstr. Appl. Anal, Article ID 840621, 14 pages (2012)Google Scholar
- 12.Ashyralyev, A., Yilmaz, S.: On the numerical solution of ultra-parabolic equations with the Neumann Condition. In: AIP Conference Proceedings, vol. 1470, pp. 240–243 (2012)Google Scholar