Abstract: 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.