A-EBDF: an adaptive method for numerical solution of stiff systems of ODEs. In this paper a one parameter predictor–corrector method, which we call it A-EBDF, is introduced and analyzed. With a modification of A-BDF and EBDF methods we propose a multistep method whose region of absolute stability is larger than those of A-BDF and EBDF methods.

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  1. Abdi, A.; Hosseini, S. A.; Podhaisky, H.: Adaptive linear barycentric rational finite differences method for stiff ODEs (2019)
  2. Secer, Aydin; Ozdemir, Neslihan; Bayram, Mustafa: A Hermite polynomial approach for solving the SIR model of epidemics (2018)
  3. 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)
  4. Kazemi Nasab, A.; Pashazadeh Atabakan, Z.; Ismail, A. I.: An accurate numerical algorithm for solving singular and nonsingular system of initial value problems on large interval (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. Biazar, Jafar; Asadi, Mohammad Ali; Salehi, Farideh: Rational homotopy perturbation method for solving stiff systems of ordinary differential equations (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, M.; Gokhale, M. Y.: Class 2 + 1 hybrid BDF-like methods for the numerical solutions of ordinary differential equations (2011)
  11. Ebadi, Moosa: A class of multistep methods based on a super-future points technique for solving IVPs (2011)
  12. Ezzeddine, Ali K.; Hojjati, Gholamreza: Hybrid extended backward differentiation formulas for stiff systems (2011)
  13. Lepik, Ü.: Haar wavelet method for solving stiff differential equations (2009)
  14. Willms, Allan R.: Parameter range reduction for ODE models using cumulative backward differentiation formulas (2007)
  15. Hojjati, G.; Ardabili, M. Y. Rahimi; Hosseini, S. M.: A-EBDF: An adaptive method for numerical solution of stiff systems of ODEs (2004)