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A Non-Iteration Solution For Solving The Backward-In-Time Two-Dimensional Burgers’ Equation With A Large Reynolds Number, Yen-Shen Chang, Yung-Wei Chen, Chein-Shan Liu, Jiang-Ren Chang

Journal of Marine Science and Technology

This article proposes a noniteration solution based on the Lie-group shooting method (LGSM) to solve the backward-in-time two-dimensional Burgers’ equation with a large Reynolds number. The backward problem is famous for seriously ill-posed cases because the solution is generally unstable and highly dependent on the input data. Small perturbations in the input data, such as random errors inherent to the measurements in the analysis, can cause large oscillations in the solution. To handle a large Reynolds number under long time spans, it is very difficult to integrate towards the time direction. To avoid time integration and numerical iteration, the noniteration …