A one-step new general meshfree scheme, which is based on radial basis functions, is presented for a viscous wave equation with variable coefficients. By constructing a simple extended radial basis function, it can be directly applied to wave propagation by using the strong form-based meshfree collocation method. There is no need to deal with the time-dependent variable particularly. Numerical results for a viscous wave equation with variable coefficients show that the proposed meshfree collocation method is simple, accurate, stable and computationally efficient.

中文翻译：

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变系数粘性波动方程的一种新的无网格策略

针对具有可变系数的粘性波动方程，提出了一种基于径向基函数的一步新的通用无网格方案。通过构造一个简单的扩展径向基函数，它可以通过使用基于强形式的无网格搭配方法直接应用于波的传播。不需要特别处理随时间变化的变量。具有可变系数的粘性波动方程的数值结果表明，所提出的无网格配置方法简单、准确、稳定且计算效率高。