A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic
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DOI: 10.1016/j.matcom.2016.03.007
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References listed on IDEAS
- Mazzia, Francesca & Nagy, A.M., 2015. "A new mesh selection strategy with stiffness detection for explicit Runge–Kutta methods," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 125-134.
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- Lolli, Gabriele, 2015. "Metamathematical investigations on the theory of Grossone," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 3-14.
- Kanovei, Vladimir & Lyubetsky, Vassily, 2015. "Grossone approach to Hutton and Euler transforms," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 36-43.
- Sergeyev, Yaroslav D., 2009. "Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3042-3046.
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Cited by:
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- Cococcioni, Marco & Pappalardo, Massimo & Sergeyev, Yaroslav D., 2018. "Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 298-311.
- Falcone, Alberto & Garro, Alfredo & Mukhametzhanov, Marat S. & Sergeyev, Yaroslav D., 2021. "A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
- Renato Leone & Giovanni Fasano & Massimo Roma & Yaroslav D. Sergeyev, 2020. "Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 554-589, August.
- Essam R. El-Zahar & José Tenreiro Machado & Abdelhalim Ebaid, 2019. "A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
- Renato De Leone & Giovanni Fasano & Yaroslav D. Sergeyev, 2018. "Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming," Computational Optimization and Applications, Springer, vol. 71(1), pages 73-93, September.
- Caldarola, Fabio, 2018. "The Sierpinski curve viewed by numerical computations with infinities and infinitesimals," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 321-328.
- Borri, Alessandro & Carravetta, Francesco & Palumbo, Pasquale, 2023. "Quadratized Taylor series methods for ODE numerical integration," Applied Mathematics and Computation, Elsevier, vol. 458(C).
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Keywords
Ordinary differential equations; Initial value problems; Taylor methods; Numerical infinitesimals; Infinity computer;All these keywords.
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