**Topic/Type**:
3. Other, Poster

###
Numerical Realization of Korteweg-de Vries and Kadomtsev-Petviashvili type Equations by High-order Accuracy Schemes

**
T.Vashakmadze**^{1, 2}, T.Kaladze^{2}, L.Tsamalashvili^{2}

*
*^{1} Javakhishvili Tbilisi State University

^{2} VIAM of Tbilisi State University

3D uniform mathematical models of continuum mechanics [1] are considered which contain Navier-Stockes equation too. Using for Navier-Stockes type equations average methods [2,ch.2] the nonlinear evolutionary differential equations of the fourth order with respect to (x,y) coordinates are obtained. These equations are the generalization of Korteweg-de Vries and Kadomtsev-Petviashvili(KP) equations. Then for these ( KP type) equations accounting to them an initial and boundary value conditions and using Bellman?s type classical linearization methods we got corresponding linear problems. These last one problems are solved by new m and n order accuracy schemes respect to mesh widths of time and spatial coordinates. The arbitrary positive numbers m and n are depending from the smoothness of unknown solutions.

[1] T.Vashakmadze.On the Basic Systems of Equations of Continuum Mechanics and SomeMathematical Problems for Anisotropic Thin-walled Structures, IUTAM Symposium on Relations of Shell, Plate, Beam, and 3D Models, Springer, 2008, 207-217

[2] T. Vashakmadze ? The Theory of Anisotropic Elastic Plates, luwer Acad. Publ. Springer-Verlafor Anisotropic hin-walled g, Dordrecht/ Boston/ London, 1999