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• W2267688751 abstract "When the given input data are corrupted by an intensive noise, most numerical methods may fail to produce acceptable numerical solutions. Here, we propose a new numerical scheme for solving the Burgers equation forward in time and backward in time. A fictitious time t is used to transform the dependent vari- able u(x;t) into a new one by (1+t)u(x;t) =:v(x;t;t), such that the original Burg- ers equation is written as a new parabolic type partial differential equation in the space of (x;t;t). A fictitious damping coefficient can be used to strengthen the sta- bility in the numerical integration of a semi-discretized ordinary differential equa- tions set on the spatial-temporal grid points. Even for a very large final time and under a large noise, the present Fictitious Time Integration Method (FTIM) can be used to retrieve the initial data very well. When the FTIM is used to solve the direct problems of Burgers equation, with a large Reynolds number and the input data being noised seriously, we can still reconstruct the solution rather accurately. This result however cannot be achieved by other conventional numerical methods. It is interesting that both the forward and backward problems of Burgers equation can be unifiedly treated by the FTIM." @default.
• W2267688751 created "2016-06-24" @default.
• W2267688751 creator A5090276712 @default.
• W2267688751 date "2009-02-01" @default.
• W2267688751 modified "2023-09-27" @default.
• W2267688751 title "A Fictitious Time Integration Method for the Burgers Equation" @default.
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• W2267688751 doi "https://doi.org/10.3970/cmc.2009.009.229" @default.
• W2267688751 hasPublicationYear "2009" @default.
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