Journal
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
Volume 23, Issue 1, Pages 135-148Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ijnsns-2020-0241
Keywords
Bona-Smith family; quintic B-spline method; solitary waves; von-Neumann technique
Funding
- National Natural Science Foundation of China [11271064]
- Natural Science Foundation of Zhejiang Province, China [LY20A010003]
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This work investigates a new numerical solution for a well-known non-linear wave equation, using the quintic B-spline collocation method. The method is shown to be unconditionally stable and efficient, with results in good agreement with the analytic solution. Physical interpretations of the results are demonstrated graphically using symbolic computation.
Our main purpose in this work is to investigate a new solution that represents a numerical behavior for one well-known nonlinear wave equation, which describes the Bona-Smith family of Boussinesq type. A numerical solution has been obtained according to the quintic B-spline collocation method. The method is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The stability of the proposed method has been discussed and presented to be unconditionally stable. The efficiency of the proposed method has been demonstrated by studying a solitary wave motion and interaction of two and three solitary waves. The results are found to be in good agreement with the analytic solution of the system. We demonstrated the physical interpretation of some obtained results graphically with symbolic computation.
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