摘要：AbstractBackgroundThis paper provides an advance numerical algorithm to solve both ordinary and partial differential equations of surface water quality models. It uses finite difference methods and structures explicit or implicit or other process forms to solve the water quality model. This study also considers the stability of solutions to obtain more accurate results among those numerical algorithms.ResultsWater quality modeling commonly manifests itself in ordinary and partial differential equations in a realistic world. This study has applied numerical solutions to simulate the changing process of water quality in one and two dimensional spaces or in multiple dimensional spaces. The solutions of these analytical methods are provided in this paper to attest the justifiability of these numerical methods. It demonstrates that the 2-dimensional Barakat-Clark numerical method can be a highly efficient tool in obtaining approximate results of ordinary and partial differential equations, which may prove difficult in finding the accurate solution by using conventional methods. At the same time, the stability analysis corroborated the convergence of those numerical solutions.ConclusionsThis study is the first attempt to compare the multiple numerical methods with the 2-D Barakat-Clark method in the water quality modeling process. The results clearly suggest that the Barakat-Clark method is better in reflecting the accuracy of the water quality modeling with stability for hydrological systems.
