无网格法求解分段连续型延迟偏微分方程

Meshless method for delay partial differential equations with piecewise continuous arguements

考虑了一类分段连续型延迟偏微分方程.首先分析了方程的解析解,给出了级数形式的解.其次采用无网格法求解了该类方程的数值解.利用θ-加权有限差分法对方程的时间变量进行离散,并利用Multiquadric(MQ)径向基函数和配点法建立了全离散格式.采用傅里叶分析法给出了数值方法稳定的条件.通过数值算例给出了方法的误差及验证了方法的有效性.

We consider a class of delay partial differential equation with piecewise continuous arguments in this paper.First,we analyze the analytical solution of the equation and give the solution in the series form.Second,we solve the numerical solution of the equation by meshless interpolation method.The time variable of the equation is discretized by theθ-weighted finite difference method,and the full dispersion scheme is established by the multiquadric(MQ)radial basis function and the collocation method.Fourier analysis gives stability conditions of the numerical method.We also compute the errors and check the validity of the numerical method by concrete examples.