An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems. An efficient algorithm for the numerical integration of large sparse systems of stiff initial value ordinary differential equations and differential-algebraic equations is described. The algorithm is constructed by embedding a standard sparse linear algebraic equation solver into a suitably modified MEBDF code. An important practical application of this algorithm is in the numerical solution of time dependent partial differential equations, particularly in two or more space dimensions, using the method of lines. A code based on this algorithm is illustrated by application to several problems of practical interest and its performance is compared to that of the standard code LSODES.

References in zbMATH (referenced in 88 articles , 1 standard article )

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  1. Costa, Pedro M. P.; Albuquerque, Duarte M. S.: A novel approach for temporal simulations with very high-order finite volume schemes on polyhedral unstructured grids (2022)
  2. Okor, T.; Nwachukwu, G. C.: High order extended boundary value methods for the solution of stiff systems of ODEs (2022)
  3. Abdi, Ali; Hojjati, Gholamreza: Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants (2021)
  4. Amin, Fahs; Zakeri, Ali; Wanko, Adrien: Time-dependent solution for natural convection in a porous enclosure using the Darcy-Lapwood-Brinkman model (2021)
  5. Bassenne, Maxime; Fu, Lin; Mani, Ali: Time-accurate and highly-stable explicit operators for stiff differential equations (2021)
  6. Esmaeelzadeh, Zahra; Abdi, Ali; Hojjati, Gholamreza: EBDF-type methods based on the linear barycentric rational interpolants for stiff IVPs (2021)
  7. Okor, T.; Nwachukwu, G. C.; Adeyeye, F. J.: Robust extended trapezoidal rules for two-point stiff and non-stiff boundary value problems (2021)
  8. Urevc, Janez; Starman, Bojan; Maček, Andraž; Halilovič, Miroslav: A novel class of collocation methods based on the weighted integral form of ODEs (2021)
  9. Eskandari, Zohreh; Dahaghin, Mohammad Shafi: Stability analysis of third derivative multi-step methods for stiff initial value problems (2020)
  10. Holst, Kevin R.; Glasby, Ryan S.; Bond, Ryan B.: On the effect of temporal error in high-order simulations of unsteady flows (2020)
  11. Tang, Xiao; Xiao, Aiguo: Improved Runge-Kutta-Chebyshev methods (2020)
  12. Abdi, A.; Hosseini, S. A.; Podhaisky, H.: Adaptive linear barycentric rational finite differences method for stiff ODEs (2019)
  13. Agarwal, P.; Ibrahim, Iman H.; Yousry, Fatma M.: G-stability one-leg hybrid methods for solving DAEs (2019)
  14. Martín-Vaquero, J.; Kleefeld, A.: ESERK5: a fifth-order extrapolated stabilized explicit Runge-Kutta method (2019)
  15. Boom, Pieter D.; Zingg, David W.: Optimization of high-order diagonally-implicit Runge-Kutta methods (2018)
  16. Izzo, Giuseppe; Jackiewicz, Zdzislaw: Generalized linear multistep methods for ordinary differential equations (2017)
  17. Movahedinejad, Akram; Hojjati, Gholamreza; Abdi, Ali: Construction of Nordsieck second derivative general linear methods with inherent quadratic stability (2017)
  18. Nasab, Masoumeh Hosseini; Hojjati, Gholamreza; Abdi, Ali: A class of methods with optimal stability properties for the numerical solution of IVPs: construction and implementation (2017)
  19. Nigro, A.; de Bartolo, C.; Crivellini, A.; Bassi, F.: Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows (2017)
  20. Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung: An error embedded method based on generalized Chebyshev polynomials (2016)

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