An efficient method for solving coupled viscous Burgers’ equations

In this paper, we propose a Reproducing Kernel Method (RKM) for solving the system of Coupled Viscous Burgers’ Equations (CVBEs). The accuracy and efficiency of the RKM depend critically on several choices: the component space, inner product, discretization points, basis functions, and overall solution strategy. As these elements are interdependent, suboptimal selections in any component can hinder the desired results. The inherent complexity of solving nonlinear PDE systems, further amplified by the structural requirements of the RKM, makes developing an effective method for this problem class particularly challenging. A further objective is to establish a systematic theoretical framework encompassing error analysis, convergence theorems, and supporting lemmas that align closely with numerical outcomes. The proposed method must also demonstrate superiority over existing approaches. Our numerical experiments confirm that these challenges have been successfully addressed, showcasing the method’s efficacy and validating the theoretical framework.