We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the framework of viscosity solutions, provided that the basis function approximations of the terminal condition and the nonlinearities are successful at each time step. A numerical experiment with a radial basis function demonstrates the convergence property.

翻译：在粘性解理论框架下，我们证明了无网格配点法对完全非线性抛物型偏微分方程终值问题的收敛性，其前提条件是终端条件及非线性项的基函数近似在每个时间步长上均成功实现。通过采用径向基函数进行的数值实验验证了该收敛特性。