The inverse operator method（IOM） is a new nonnumerical method for solving the strongly nonlinear problems. It is used to analyze linearly graded p-n junctions. The analysis problems are formulated as one-dimensional nonlinear Poisson’ s equations

and the IOM is used to solve these strongly nonlinear ordinary differential equations. By using the symbolic calculus software （Mathematica）

the approximate analytic solutions are calculated. Also

the error analysis for these approximate solutions is carried out. The simulated results are accurate and reliable

which has realized the quantitative analysis of linearly graded p-n junctions and will contribute to making a thorough study of p-n junctions. Our research results indicate that the IOM has some advantages

and that it will open up a new way for the numerical analysis of semiconductor devices.