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Numerical methods for singular nonlinear integro-differential equations
Institution: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, Faculty of Science-Blqarn Campus, Bisha University, Saudi Arabia;2. Department of Mathematics, Faculty of Science-Jeddah University, Jeddah, Saudi Arabia;3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China;4. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL-35762, 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. Institute of Physics Belgrade, Pregrevica 118, 11080, Zemun, Serbia;1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Punjab, Pakistan;2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematical Sciences, UAEU P O Box 15551, Al-Ain, United Arab Emirates
Abstract:For the numerical integration of singular nonlinear integro-differential equations we consider fractional linear multistep methods. We prove convergence of these methods and discuss their stability (as an extension of A-stability for stiff differential equations). Numerical experiments with the Basset equation are included.
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