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Program generation method for calculation of a Poisson equation, diffusion equation, or like partial differential equation performed on irregularly dispersed grid points
Program generation method for calculation of a Poisson equation, diffusion equation, or like partial differential equation performed on irregularly dispersed grid points
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机译:用于对不规则分散的网格点执行的泊松方程,扩散方程或类似偏微分方程的计算的程序生成方法
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摘要
In order to provide an approximate solution having high accuracy to a given partial differential equation made up of one of a Poisson equation, diffusion equation or other partial differential equation similar in form to a Poisson or diffusion equation, the given equation being applied on a plurality of grid points dispersed at irregular intervals, a program is generated in which not only the dependent variable of the original equation is used, but in addition first order derivatives thereof also are input independently as additional dependent variables, the program thereby serving to execute and solve discretized equations using discretized expressions made up of high accuracy second and third order derivative terms of a dependent variable of the given partial differential equation.
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