Breaking the limits: The Taylor series method

DOI10.1016/j.amc.2011.02.080zbMath1219.65064OpenAlexW2071031751MaRDI QIDQ548357

Roberto Barrio, Fernando Blesa, Alberto Abad, Marcos Rodríguez

Publication date: 28 June 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.02.080

zbMATH Keywords

numerical examplesautomatic differentiationvariational equationsTaylor series methodfreeware softwarebox propagationhigh-precision integration of ODEspropagation of errors

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Packaged methods for numerical algorithms (65Y15) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (20)

Computational complexity of solving polynomial differential equations over unbounded domains ⋮ Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science ⋮ Approximation of solutions of polynomial partial differential equations in two independent variables ⋮ New algorithms for Taylor coefficients of indefinite integrals and their applications ⋮ A database of rigorous and high-precision periodic orbits of the Lorenz model ⋮ A Taylor series method for the solution of the linear initial-boundary-value problems for partial differential equations ⋮ Convergent power series of \(\operatorname{sech}(x)\) and solutions to nonlinear differential equations ⋮ OpenCL parallel integration of ordinary differential equations: applications in computational dynamics ⋮ Quadratized Taylor series methods for ODE numerical integration ⋮ A database of high precision trivial choreographies for the planar three-body problem ⋮ Uncertainty propagation or box propagation ⋮ High-precision computation: mathematical physics and dynamics ⋮ Status of the differential transformation method ⋮ A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic ⋮ Automatic implementation of the numerical Taylor series method: a \textsc{Mathematica} and \textsc{Sage} approach ⋮ On approximate implicit Taylor methods for ordinary differential equations ⋮ A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder ⋮ Truncation bounds for differentially finite series ⋮ Computability of Differential Equations ⋮ High-precision arithmetic in mathematical physics

Uses Software

• Mathematica
• mctoolbox
• TIDES
• Cosy
• ATOMFT
• Taylor
• DAETS
• RODES

Cites Work

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