Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions | Zendy

Pablo Suarez | Zendy; J. Morales | Zendy

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Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions

Author(s) -

Pablo Suarez,

J. Morales

Publication year - 2014

Publication title -

international journal of partial differential equations

Language(s) - English

Resource type - Journals

eISSN - 2356-7082

pISSN - 2314-6524

DOI - 10.1155/2014/407387

Subject(s) - discretization , nonlinear system , mathematical analysis , mathematics , collocation method , radial basis function , partial differential equation , collocation (remote sensing) , ordinary differential equation , basis (linear algebra) , orthogonal collocation , basis function , runge–kutta methods , numerical analysis , differential equation , physics , geometry , computer science , quantum mechanics , machine learning , artificial neural network

We obtain the numerical solution of a Boussinesq system fortwo-way propagation of nonlinear dispersive waves by using the meshlessmethod, based on collocation with radial basis functions. The system ofnonlinear partial differential equation is discretized in space by approximatingthe solution using radial basis functions. The discretization leads to asystem of coupled nonlinear ordinary differential equations. The equationsare then solved by using the fourth-order Runge-Kutta method. A stabilityanalysis is provided and then the accuracy of method is tested by comparingit with the exact solitary solutions of the Boussinesq system. In addition, theconserved quantities are calculated numerically and compared to an exactsolution. The numerical results show excellent agreement with the analyticalsolution and the calculated conserved quantities

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