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首页> 外文期刊>International Journal of Partial Differential Equations >Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions
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Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions

机译：径向色散函数在非线性色散波双向传播中的数值解

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摘要

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.
机译：我们在基于径向基函数的基础上，采用无网格方法，获得了非线性色散波双向传播的Boussinesq系统的数值解。通过使用径向基函数逼近解，可以将非线性偏微分方程组离散化。离散导致耦合非线性常微分方程的系统。然后使用四阶Runge-Kutta方法求解方程。提供稳定性分析，然后通过与Boussinesq系统的精确孤立解进行比较来测试方法的准确性。另外，保守量通过数字计算并与精确解进行比较。数值结果表明与解析溶液和计算的守恒量吻合良好。

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