Convergence of meshfree collocation methods for fully nonlinear parabolic equations
Convergence of meshfree collocation methods for fully nonlinear parabolic equations
复制标题
全非线性抛物型方程无网格配置方法的收敛性
DOI：
10.1007/s00211-016-0852-8
复制
发表时间：
2016
影响因子：
2.1
通讯作者：
Yumiharu Nakano
中科院分区：
文献类型：
--
作者：
小國仁嗣;齋藤保久;Yasuhisa SAITO;Yumiharu Nakano
在粘性解的框架下，证明了完全非线性抛物型偏微分方程终值问题的无网格配置法的收敛性，条件是在每个时间步上对终值条件和非线性项的基函数逼近都是成功的.一个径向基函数的数值实验证明了收敛性。
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.