A new numerical application of the generalized Rosenau-RLW equation
نویسندگان
1 Scientific Department, Azov-Black Sea Engineering Institute of Don State Agricultural University, 347740, 21 Lenin Str., Zernograd, Russian Federation
2 Department of Technology and Mechanization of Agriculture, Azov-Black Sea Engineering Institute of Don State Agricultural University, 347740, 21 Lenin Str., Zernograd, Russian Federation
3 Department of Technical Service in Agro-Industrial Complex, Azov-Black Sea Engineering Institute of Don State Agricultural University, 347740, 21 Lenin Str., Zernograd, Russian Federation
4 Engineering and Transfer Center, Azov-Black Sea Engineering Institute of Don State Agricultural University, 347740, 21 Lenin Str., Zernograd, Russian Federation
5 LLC Research and Production Inculcation Firm 'Tenzor-T'", 347916, 11-49 Vishnevaya Str. Taganrog, Russian Federation
doi
10.24200/sci.2018.50490.1721چکیده
In this article, a collocation fi nite element method based on septic B-splines as a tool has been carried out to obtain the numerical solutions of the nonlinear generalized Rosenau-RLW equation. One of the advantages of this method is that when the bases are chosen at a high degree, better numerical solutions are obtained. Effectiveness of the method is demonstrated by solving the equation with various initial and boundary conditions. Also, in order to detect the performance of the method we have computed L2 and L1 error norms and two lowest invariants IM and IE: The obtained numerical results have been compared with some of those in the literature for similar parameters. This comparison clearly shows that the obtained results are better than and found in good conformity with the some earlier results. Stability analysis denotes that our algorithm, based on a Crank Nicolson approximation in time, is unconditionally stable.
