On irregular discretization of poisson's equation


Zorica Uzelac, Dragoslav Herceg




In this paper an irregular discretization of the boundary value problem ($GZ$) is given. An irregular mash $\bar G_{h,k}$ is given by (2), (3), (4) and (5). Using formulas (7), (8) and (9) a discrete analogone ($DGZ$) for ($GZ$) is formed. The inverse monotonicity of matrix $A_{h,k}$ is proved under assumptions (i) and (ii), Theorem 1. From the preceding, it followed that there exists a unique solution of ($DGZ$) and that this solution converges to the solution of ($GZ$) when the number of points of mash $\bar G_{h,k}$ tends to infinity (i.e. $m\to\infty$ and $n\to\infty$). In \S5, a numerical example is given.