Abstract
MATLAB software package offers a set of open source adaptative step functions for solving Ordinary Differential Equations (ODEs) which are easy to use by non-experts. Two of these functions are the well-known ode45 and ode15s. The ode45 is adequate when solving nonstiff problems, while the ode15s is recommended for stiff problems. Due to the wide utilization of MATLAB in science and engineering and taking into account that some issues of interest are found, we have studied the numerical methods in which these two ode solvers are based, describing the error estimation and the step size control implemented in the codes. First and second order linear ODEs are solved as two extreme examples to characterize the functions response and finally, some conclusions related to the stability of these solvers and the inefficiency of ode15s in stiff problems with pure imaginary eigenvalues are presented.
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Acknowledgements
The first author was partially funded by the Basque Government Consolidated Research Group Grant IT649-13 on “Mathematical Modeling, Simulation, and Industrial Applications (M2SI)”.
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Celaya, E.A., Aguirrezabala, J.J.A. (2015). Construction of MATLAB adaptative step ODE solvers. In: Jeribi, A., Hammami, M., Masmoudi, A. (eds) Applied Mathematics in Tunisia. Springer Proceedings in Mathematics & Statistics, vol 131. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18041-0_23
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DOI: https://doi.org/10.1007/978-3-319-18041-0_23
Publisher Name: Birkhäuser, Cham
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