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A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation. (English) Zbl 1243.76069
Summary: We employ the boundary-only meshfree method to find out numerical solution of the classical Boussinesq equation in one dimension. The proposed method in the current paper is a combination of boundary knot method and meshless analog equation method. The boundary knot technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. Also, we use the meshless analog equation method to replace the nonlinear governing equation with an equivalent nonhomogeneous linear equation. A predictor-corrector scheme is proposed to solve the resulted differential equation of the collocation. The numerical results and conclusions are obtained for both the `good’ and the `bad’ Boussinesq equations.

MSC:
76M25Other numerical methods (fluid mechanics)
65M99Numerical methods for IVP of PDE
35Q35PDEs in connection with fluid mechanics
35C08Soliton solutions of PDE
35C07Traveling wave solutions of PDE
Software:
MATLAB expm
WorldCat.org
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References:
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