“…Let be the grid ratio parameter. A Numerov type approximation with accuracy of O ( k 2 + k 2 h 2 + h 4 ) for the solution of for l , m = 1(1) N − 1, 0 < j ≤ J may be written as where a = α 2 k 2 , b = β 2 k 2 , and δ t and μ t are central and averaging operators with respect to time direction, respectively. Similarly, operators with respect to spatial directions are defined.…”