Abstract: In this accompanying study,we compare and analyze the differences in stability,convergence,precision and efficiency resulting from the use of two methods in the solution of the one-dimensional model for coupling surface water flow with solute transport for border fertigation(1-DMCSWFSTBF).The first method is the hybrid numerical method,while the second one is the Roe finite volume method.Results show that the hybrid numerical method produces better numerical stability and convergence compared to the Roe finite volume method.Under the same circumstances of measurement,the former method is 2.5 times more computationally effective than the latter one,and the corresponding average relative error and water balance error are also improved.Thus,1-DMCSWFSTBF based on the hybrid numerical method can significantly increase the computational stability and convergence,and can effectively improve the computational precision and efficiency.The model can be used as an effective simulation tool for the design and performance evaluation of border fertigation systems.