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. Izzo, Giuseppe; Jackiewicz, Zdzislaw: Generalized linear multistep methods for ordinary differential equations (2017)
  2. Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung: An error embedded method based on generalized Chebyshev polynomials (2016)
  3. Kleefeld, B.; Martín-Vaquero, J.: SERK2v3: Solving mildly stiff nonlinear partial differential equations (2016)
  4. Martín-Vaquero, J.; Kleefeld, B.: Extrapolated stabilized explicit Runge-Kutta methods (2016)
  5. Nguyen-Ba, Truong: On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs (2016)
  6. Nguyen-Ba, Truong; Giordano, Thierry: On variable step highly stable 4-stage Hermite-Birkhoff solvers for stiff ODEs (2016)
  7. Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia: Efficient implementation of Radau collocation methods (2015)
  8. Ibrahim, Iman H.; Yousry, Fatma M.: Hybrid special class for solving differential-algebraic equations (2015)
  9. 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)
  10. Ebadi, Moosa; Gokhale, M.Y.: Solving nonlinear parabolic PDEs via extended hybrid BDF methods (2014)
  11. Nazari, Farshid; Mohammadian, Abdolmajid; Charron, Martin; Zadra, Ayrton: Optimal high-order diagonally-implicit Runge-Kutta schemes for nonlinear diffusive systems on atmospheric boundary layer (2014)
  12. Nigro, Alessandra; De Bartolo, Carmine; Bassi, Francesco; Ghidoni, Antonio: Up to sixth-order accurate A-stable implicit schemes applied to the discontinuous Galerkin discretized Navier-Stokes equations (2014)
  13. Musa, H.; Suleiman, M.B.; Ismail, F.; Senu, N.; Ibrahim, Z.B.: An accurate block solver for stiff initial value problems (2013)
  14. Nazari, Farshid; Mohammadian, Abdolmajid; Zadra, Ayrton; Charron, Martin: A stable and accurate scheme for nonlinear diffusion equations: application to atmospheric boundary layer (2013)
  15. Nordström, Jan; Lundquist, Tomas: Summation-by-parts in time (2013)
  16. Sergeyev, Yaroslav D.: Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically (2013)
  17. D’Ambrosio, Raffaele; Izzo, Giuseppe; Jackiewicz, Zdzislaw: Perturbed MEBDF methods (2012)
  18. Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline: A test set for stiff initial value problem solvers in the open source software R: Package \bfdeTestSet (2012)
  19. Soetaert, Karline; Cash, Jeff; Mazzia, Francesca: Solving differential equations in R. (2012)
  20. Zawawi, I.S.M.; Ibrahim, Z.B.; Ismail, F.; Majid, Z.A.: Diagonally implicit block backward differentiation formulas for solving ordinary differential equations (2012)

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