许多工程问题可通过带有未知参数的抛物方程求解.因此,发展高精度数值方法求解这类反问题非常重要.本文提出一种交替方向隐格式(ADI)的三层线性化组合紧致差分(CCD)格式求解带控制参数的二维非定常反应扩散方程.该方法在时间上达到二阶精度,空间上达到六阶精度.在每个ADI迭代步,只需求解一个块三对角系统,可通过块Thomas算法快速求解.此外,我们严格证明在周期性边界条件下,CCD-ADI方法解的存在性和唯一性.最后,通过与已有空间四阶方法对比,用数值算例验证新方法的无条件稳定性、精度与效率.“,”Many engineering problems can be modelled by parabolic differential equations with unknown parameters.It is often quite important to develop highly accurate numerical methods for solving these inverse problems.In this pa-per,we propose a linearized three-level combined compact difference (CCD) scheme with the alternating direction implicit (ADI) method for solving the two-dimensional unsteady reaction-diffusion equation with a control parameter.The proposed method is sixth-order accurate in space and second-order accurate in time.The resulting linear system at each ADI step is a block tridiagonal system which can be solved effectively by the block Thomas algorithm.In addi-tion,we rigorously prove the existence and the uniqueness of the solution of the CCD-ADI method under the periodic boundary conditions.Finally,numerical tests are carried out to show the unconditional stability,the accuracy and effi-ciency of the proposed method compared with the existing spatial fourth-order method.