Accurate numerical resolution of transients in initial-boundary value problems for the heat equation |
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| Affiliation: | 1. Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave., P.O. Box 15875-4413, Tehran, Iran;2. Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. National Engineering Research Center for Intelligent Electrical Vehicle Power System, Qingdao University, Qingdao, Shandong 266071, China;3. School of Electromechanical Engineering, Qingdao University, Qingdao 266071, China |
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| Abstract: | If the initial and boundary data for a PDE do not obey an infinite set of compatibility conditions, singularities will arise in the solution at the corners of the initial time–space domain. For dissipative equations, such as the 1-D heat equation or 1-D convection–diffusion equations, the impacts of these singularities are short lived. However, they can cause a very severe loss of numerical accuracy if we are interested in transient solutions. The phenomenon has been described earlier from a theoretical standpoint. Here, we illustrate it graphically and present a simple remedy which, with only little extra cost and effort, restores full numerical accuracy. |
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