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A modified Lyapunov method and its applications to ODE
  • Manuel Gadella,
  • Luis Pedro Lara
Manuel Gadella
University of Valladolid

Corresponding Author:[email protected]

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Luis Pedro Lara
Instituto de Física Rosario Rosario
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Here, we propose a method to obtain local analytic approximate solutions of ordinary differential equations with variable coefficients, or even some non-linear equations, inspired in the Lyapunov method, where instead of polynomial approximations, we use truncated Fourier series with variable coefficients as approximate solutions. In the case of equations admitting periodic solutions, an averaging over the coefficients gives global solutions. We show that, under some restrictive condition, the method is equivalent to the Picard-Lindel\”of method. After some numerical experiments showing the efficiency of the method, we apply it to equations of interest in Physics, in which we show that our method possesses an excellent precision even with low iterations.
16 Feb 2022Submitted to Mathematical Methods in the Applied Sciences
18 Feb 2022Submission Checks Completed
18 Feb 2022Assigned to Editor
21 Feb 2022Reviewer(s) Assigned
01 Jun 2022Review(s) Completed, Editorial Evaluation Pending
02 Jun 2022Editorial Decision: Revise Minor
03 Jun 20221st Revision Received
06 Jun 2022Submission Checks Completed
06 Jun 2022Assigned to Editor
07 Jun 2022Reviewer(s) Assigned
08 Jul 2022Review(s) Completed, Editorial Evaluation Pending
10 Jul 2022Editorial Decision: Revise Minor
17 Jul 20222nd Revision Received
18 Jul 2022Submission Checks Completed
18 Jul 2022Assigned to Editor
18 Jul 2022Review(s) Completed, Editorial Evaluation Pending
19 Jul 2022Editorial Decision: Accept
28 Jul 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8598