On computing smooth solutions of problems with large lipschitz constants |
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| Institution: | 1. Department of Mathematics, Massachusetts Institute of Technology, United States of America;2. Departments of Statistics and Mathematics, Columbia University, United States of America;3. Department of Statistics, Columbia University, United States of America;1. Department of Physics, Government Degree College Dhaliara, District Kangra, Himachal Pradesh 177103, India;2. Department of Chemical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India;3. Department of Physics, DAV College, Jalandhar, Punjab 144008, India;4. CSIR-Institute of Minerals and Materials Technology, Bhubaneswar 751013, India |
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| Abstract: | We investigate how one can construct numerical methods for computing smooth solutions of ODE's which potentially possess fast growing or decaying solutions. We do not want to use a global method (which computes a solution on the entire relevant interval first), but rather a procedure that obtains numerical values in a marching algorithm. It is shown how this can be achieved by both implicit and explicit integrators, for which some detailed analysis is given. Some numerical examples are also included. |
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