In this paper

the existence of the optimal weighted factor in the weighted implicit scheme of one dimensional heat diffusion equation is analysed.Also

we show the graphic relationship between the optimal weighted factor and the mesh ratio

the time step

the space step

the number of iteration levels in time direction

and the number of space meshs.We point out that when it is difficult to determine the number of time levels in computing the numerical solution with a definite ratio

quadratic Lagrange\'s interpolation can be employed to obtain a satisfactory solution with high accuracy.Furthermore

we have discussed the feasibility of high accuracy and high efficiency numerical computation with a properly larger ratio.Finally

we point out that the case when \$r=120\$ and \$θ=12-112r

\$ the truncation error is \$O(h\+6)\+\{[1]\}

\$ is a special one about the optimal weighted factor problem.