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.

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  1. Holst, Kevin R.; Glasby, Ryan S.; Bond, Ryan B.: On the effect of temporal error in high-order simulations of unsteady flows (2020)
  2. Tang, Xiao; Xiao, Aiguo: Improved Runge-Kutta-Chebyshev methods (2020)
  3. Abdi, A.; Hosseini, S. A.; Podhaisky, H.: Adaptive linear barycentric rational finite differences method for stiff ODEs (2019)
  4. Agarwal, P.; Ibrahim, Iman H.; Yousry, Fatma M.: G-stability one-leg hybrid methods for solving daes (2019)
  5. Martín-Vaquero, J.; Kleefeld, A.: ESERK5: a fifth-order extrapolated stabilized explicit Runge-Kutta method (2019)
  6. Boom, Pieter D.; Zingg, David W.: Optimization of high-order diagonally-implicit Runge-Kutta methods (2018)
  7. Izzo, Giuseppe; Jackiewicz, Zdzislaw: Generalized linear multistep methods for ordinary differential equations (2017)
  8. 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)
  9. Nigro, A.; de Bartolo, C.; Crivellini, A.; Bassi, F.: Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows (2017)
  10. Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung: An error embedded method based on generalized Chebyshev polynomials (2016)
  11. Kleefeld, B.; Martín-Vaquero, J.: SERK2v3: Solving mildly stiff nonlinear partial differential equations (2016)
  12. Martín-Vaquero, J.; Kleefeld, B.: Extrapolated stabilized explicit Runge-Kutta methods (2016)
  13. Nguyen-Ba, Truong: On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs (2016)
  14. Nguyen-Ba, Truong; Giordano, Thierry: On variable step highly stable 4-stage Hermite-Birkhoff solvers for stiff ODEs (2016)
  15. Noventa, G.; Massa, F.; Bassi, F.; Colombo, A.; Franchina, N.; Ghidoni, A.: A high-order discontinuous Galerkin solver for unsteady incompressible turbulent flows (2016)
  16. Bassi, F.; Botti, L.; Colombo, A.; Ghidoni, A.; Massa, F.: Linearly implicit Rosenbrock-type Runge-Kutta schemes applied to the discontinuous Galerkin solution of compressible and incompressible unsteady flows (2015)
  17. Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia: Efficient implementation of Radau collocation methods (2015)
  18. Eliasson, Peter; Weinerfelt, Per: High-order implicit time integration for unsteady turbulent flow simulations (2015)
  19. Ibrahim, Iman H.; Yousry, Fatma M.: Hybrid special class for solving differential-algebraic equations (2015)
  20. Nguyen-Ba, Truong; Giordano, Thierry; Vaillancourt, Rémi: Three-stage Hermite-Birkhoff solver of order 8 and 9 with variable step size for stiff ODEs (2015)

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