Document Details Document Type : Article In Journal  Document Title : Petrov-Galerkin method and K(2, 2) equation Petrov-Galerkin method and K(2, 2) equation   Subject : Mthematics  Document Language : English  Abstract : In this paper a Petrov-Galerkin method is used to derive a numerical solution for the K(2, 2) equation, where we have chosen cubic B-splines as test functions and piecewise linear functions as trial functions. The product approximation technique is applied to the nonlinear terms. A Crank-Nicolson scheme is used to discertize in time. A nonlinear pentadiagonal system is obtained. We solve this system by Newton's method and a linearization technique. The accuracy and stability of the scheme have been investigated. The single compacton solution and the conserved quantities are used to assess the accuracy of the scheme. The interaction of two compactons are displayed and the numerical results have shown that this compacton exhibits a soliton-like solution.  ISSN : 0020-7160  Journal Name : International Journal of Computer Mathematics, Volume 83, Issue 3, 1 March 2006, Pages 331-343  Volume : 83  Issue Number : 3  Publishing Year : 2006 AH 2006 AD  Number Of Pages : 12  Article Type : Article  Added Date : Thursday, October 15, 2009  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email داود سليمان محمد مشاط Daoud Suleiman Mashat Researcher Doctorate dmashat@kau.edu.sa لؤي أحمد حسن وزان Luwai Ahmed Wazzan Researcher Doctorate lwazzan@hotmail.com محمدسعيد يوسف حموده اسماعيل Ismail, M.S Researcher Doctorate msismail@kau.edu.sa Back To Researches Page