A new theoretical and computational method, which can analyze uniformly the working of slow wave oscillators with various shapes of the waveguide, is developed. Time evolution of nonlinear boundary value problems in 2D space are reduced to 1D space boundary value problems by the power expansion method, and the reduced equations can be solved numerically by the new numerical scheme HIDM (higher order implicit difference method) with high accuracy. Dynamics of the backward wave oscillator driven by an intense relativistic electron beam are analyzed by this method. It is found that a throttled shape waveguide is preferable to obtain uniform output power of microwave.