This paper presents a meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD). The algorithm is used for finding the approximate solution of nonlinear anomalous reaction–diffusion models. The time discretization procedure is carried out by means of a weighted discrete scheme covering second-order approximation, while the spatial discretization is accomplished using the RBF-FD. The theoretical discussion validates the stability and convergence of the time-discretized formulation which are analyzed in the perspective to the $H^1$-norm. This approach benefits from a local collocation technique to estimate the differential operators using the weighted differences over local collection nodes through the RBF expansion. Two test problems illustrate the computational efficiency of the approach. Numerical simulations highlight the performance of the method that provides accurate solutions on complex domains with any distribution node type.

本文提出了一种基于从局部径向基函数（RBF-FD）导出的有限差分格式的无网格方法。该算法用于寻找非线性异常反应-扩散模型的近似解。时间离散化过程是通过覆盖二阶近似的加权离散方案来执行的，而空间离散化是使用 RBF-FD 完成的。理论讨论验证了时间离散化公式的稳定性和收敛性。$H^1$-规范。这种方法受益于局部搭配技术，通过 RBF 扩展使用局部收集节点上的加权差异来估计差分算子。两个测试问题说明了该方法的计算效率。数值模拟突出了该方法的性能，该方法在具有任何分布节点类型的复杂域上提供准确的解决方案。