Adaptive step size controllers based on Runge-Kutta and linear-neighbor methods for solving the non-stationary heat conduction equation
Author:
Affiliation:
1. University of Miskolc, Institute of Physics and Electrical Engineering, Hungary
2. Department of Mathematics, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India
Abstract
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability
Reference28 articles.
1. E. Kovács, Á. Nagy, M. Saleh, A set of new stable, explicit, second order schemes for the non-stationary heat conduction equation, Mathematics, 9 (2021), 2284. https://doi.org/10.3390/math9182284
2. E. Kovács, A class of new stable, explicit methods to solve the non‐stationary heat equation, Numer Methods Partial Differ Equ, 37 (2021), 2469–2489. https://doi.org/10.1002/num.22730
3. E. Kovács, Á. Nagy, M. Saleh, A new stable, explicit, third‐order method for diffusion‐type problems, Adv Theory Simul, 5 (2022), 2100600. https://doi.org/10.1002/adts.202100600
4. S. Savović, B. Drljača, A. Djordjevich, A comparative study of two different finite difference methods for solving advection–diffusion reaction equation for modeling exponential traveling wave in heat and mass transfer processes, Ricerche di Matematica, 71 (2022), 245–252. https://doi.org/10.1007/s11587-021-00665-2
5. S. Conde, I. Fekete, J. N. Shadid, Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods, [Preprint], (2018)[cited 2023 Mar 29 ]. Available from: https://doi.org/10.48550/arXiv.1806.08693.
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