【摘要】 本文用双重调和级数解求差分形式Poisson方程(1)的最好近似解.求得在4<λ_x/d,λ_y/d<12(λ_x=λ_y是波长,d是格距)的范围内,φ的绝对平方误差最小初极近似解答是(16)式而φ的相对平方误差最小的解是(17)式.绝对平方误差与相对平方误差都比较小的是(18)式,或更简单的(23)式.本文也证明Белоусов的近似式(九点上的局部格林函数)(19)式就是(20)式,并且它的近似程度很差,完全可用(24)式代替.之后又讨论了(21)式的近似程度.根据本文的结果我们可以不用(6)或(19)式而用更好的(18)代替.这样至少可以减少一半算术运算.这对于计算时间的缩短是有用的.更多还原

【Abstract】 Best approximate solutions for finite-difference Poisson equation are obtained in this paper by using double-harmonic series solution.The first approximate solution with least square absolute error in the interval 4≤λ_x/d, λ_y/d≤12 is given by (16) and the same with least square relative error is given by (17).An intermediate solution is obtained as (18) or simply (23). It is also proved that the nine-point formula given by ???????? is equvilent to (20),and it could be replaced by the first approximation formula (24) with equal accuracy.The accuracy of (21) is shown to be unsatisfactory. It is concluded that formula (18) gives the best solution with arithmetic operations only half as much as that needed for formula (19).An example of actual computation for 500mb height tendency is given,which shows that the result obtained from formula (18) is better than that obtained from (19) or(7).更多还原