Recovering a source term in the time-fractional Burgers equation by an energy boundary functional equation |
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| Institution: | 1. Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China;2. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 202-24, Taiwan;3. Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 202-24, Taiwan |
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| Abstract: | An inverse source problem for the recovery of an unknown space–time dependent source term of a time-fractional Burgers equation is solved in the paper. By using the prescribed boundary data, a sequence of boundary functions is derived, which together with the zero element constitute a linear space. An energy boundary functional equation is derived in the linear space, of which the time-dependent energy is preserved for each energy boundary function. The iterative algorithm used to recover the unknown source with energy boundary functions as the bases is developed, which is robust and convergent fast. |
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| Keywords: | Time-fractional Burgers equation Space and time dependent source Energy boundary functions Energy functional equation Iterative method |
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