A. Abdi, S.A. Hosseini and H. Podhaisky, The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids
,
Numerical Algorithms
, (2024)
,
,
Backward differential formulae (BDF) are the basis of the highly
efficient schemes for the numerical solution of stiff ordinary differen-
tial equations for decades. An alternative multistep schemes (RBDF)
based on barycentric rational interpolation is proposed. Specifically,
robust new methods of orders 1 to 5 are derived. The local trun-
cation error is analyzed for variable stepsizes in order to implement
a variable order, variable stepsize prototype in Matlab. Aspects of
the implementation are addressed in detail. Numerical experiments
illustrate that the RBDF code compares well with Matlab’s ode15s.
A. Abdi, J.-P. Berrut and S. A. Hosseini , Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations
,
Accepted for publication in Applied Numerical Mathematics
, (2022)
,
,
A. Abdi, S.A. Hosseini and H. Podhaisky, Numerical methods based on the Floater–Hormann interpolants for stiff VIEs
,
Numerical Algorithms
, (2020)
,
85
,
867–886
A. Abdi, S.A. Hosseini and H. Podhaisky, Adaptive linear barycentric rational finite differences method for stiff ODEs
,
Journal of Computational and Applied Mathematics
, (2019)
,
357
,
204-214
A. Abdi and S. A. Hosseini, The barycentric rational difference-quadrature scheme for system of Volterra integro-differential equations
,
SIAM Journal on Scientific Computing
, (2018)
,
40
,
A1936-A1960
A. Abdi, J.-P. Berrut and S. A. Hosseini , The linear barycentric rational method for a class of delay Volterra integro-differential equations
,
Journal of Scientific Computing
, (2017)
,
75
,
1557-1575
علی عبدی و سید احمد حسینی، روشهای عددی همتافته و متقارن برای حل عددی برخی مدل¬های ریاضی اجرام سماوی
،
پژوهش های نوین در ریاضی
، (1396)
،
11
،
109-118
S. A. Hosseini and A. Abdi, On the numerical stability of the linear barycentric rational quadrature method for Volterra integral equations
,
Applied Numerical Mathematics
, (2016)
,
100
,
1-13
S. A. Hosseini, S. Shahmorad, F. Talati, A matrix based method for two dimensional nonlinear Volterra-Fredholm integral equations
,
Numerical Algorithms
, (2015)
,
68
,
511-529
J.-P. Berrut, S. A. Hosseini and G. Klein, The linear barycentric rational quadrature method for Volterra integral equations
,
SIAM Journal on Scientific Computing
, (2014)
,
36
,
A105--A123
S.A.Hosseini, S.Shahmorad and A. Tari, Existence of an Lp-solution for two dimensional integral equations of the Hammerstein type
,
Bulletin of the Iranian Mathematical Society
, (2014)
,
40
,
851-862
S.A.Hosseini, S.Shahmorad and H.Masoumi, Extension of the operational Tau method for solving 1-D nonlinear transient heat conduction equations
,
Journal of King Saud University-Science
, (2013)
,
25
,
283-288