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| Meshless method for delay partial differential equations with piecewise continuous arguments |
| Received:December 17, 2019 Revised:June 13, 2020 |
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| DOI：10.7511/jslx20191217001 |
| KeyWord:delay partial differential equation meshless interpolation method θ-weighted finite difference method multiquadric (MQ) radial basis function stability |
| Author | Institution |
| 钟霖 |
东北林业大学 理学院, 哈尔滨 |
| 马淑芳 |
东北林业大学 理学院, 哈尔滨 |
| 莱蒙 |
东北林业大学 理学院, 哈尔滨 |
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| Abstract: |
| A meshless method is a numerical method for solving partial differential equations based on scatter information.It can reduce or completely eliminate the dependence on the grid of the FEM,and the numerical implementation is more flexible.Therefore,the meshless interpolation method based on radial basis function is considered to solve a class of delay partial differential equations with piecewise continuous arguments.Firstly,the θ-weighted finite difference method is used to obtain the time-discrete scheme of the equation,then the spatial derivative is approximated by meshless interpolation method based on radial basis function,and the fully discrete numerical scheme is obtained.The basis function adopted is MQ radial basis function,which is superior to other radial basis functions in precision and stability.Secondly,the stability of the method is analyzed by using the Fourier analysis method,and the stability conditions of the method are obtained,which are only related to the time step.Finally,the convergence and stability of the method are verified by numerical examples,which show the effectiveness and applicability of the method. |
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