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Solution of the Burgers equation using an implicit linearizing transformation
Authors:Fayequa B Majid  Arjuna I Ranasinghe
Institution:1. Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia;2. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;1. Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt;2. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk, Cairo, Egypt;3. Department of Physics and Engineering Mathematics, Higher Institute of Engineering and Technology, Tanta, Egypt;4. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA;5. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;7. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey;8. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;9. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan;2. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;3. Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia;4. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;6. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Mechanical Engineering, KU Leuven, 3001 Leuven, Belgium;2. Department of Mechanical and Civil Engineering, Purdue University Northwest, 46323 Hammond, IN, USA
Abstract:The initial-boundary-value problem on the semi-infinite interval and on a finite interval for the Burgers equation ut = uxx + 2uxu is solved using a stream function ? and a linearizing transformation w = e?. The transformation reduces the equation to a heat equation with appropriate initial and homogeneous time-dependent linear boundary conditions. One advantage of this method is that we never need to find an explicit expression for ? in our computations.
Keywords:
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