Computation of higher order Lie derivatives on the infinity computer
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Publication:2199789
DOI10.1016/j.cam.2020.113135zbMath1451.65090OpenAlexW3047338125WikidataQ114202043 ScholiaQ114202043MaRDI QIDQ2199789
Felice Iavernaro, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev, Francesca Mazzia
Publication date: 14 September 2020
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://philarchive.org/rec/IAVCOH
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical differentiation (65D25)
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Uses Software
Cites Work
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- Metamathematical investigations on the theory of grossone
- A classification of one-dimensional cellular automata using infinite computations
- Computing sums of conditionally convergent and divergent series using the concept of grossone
- Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
- DNAD, a simple tool for automatic differentiation of Fortran codes using dual numbers
- Higher order numerical differentiation on the infinity computer
- Taking the Pirahã seriously
- Nonlinear control systems.
- Using grossone to count the number of elements of infinite sets and the connection with bijections
- Planar methods and grossone for the conjugate gradient breakdown in nonlinear programming
- Conjugate-symplecticity properties of Euler-Maclaurin methods and their implementation on the infinity computer
- Iterative grossone-based computation of negative curvature directions in large-scale optimization
- Solving the lexicographic multi-objective mixed-integer linear programming problem using branch-and-bound and grossone methodology
- On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales
- The exact measures of the Sierpiński \(d\)-dimensional tetrahedron in connection with a Diophantine nonlinear system
- A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic
- Independence of the grossone-based infinity methodology from non-standard analysis and comments upon logical fallacies in some texts asserting the opposite
- On a class of conjugate symplectic Hermite-Obreshkov one-step methods with continuous spline extension
- Numerical infinities and infinitesimals: methodology, applications, and repercussions on two Hilbert problems
- Lexicographic multi-objective linear programming using grossone methodology: theory and algorithm
- Numerical infinitesimals in a variable metric method for convex nonsmooth optimization
- Computation of multiple Lie derivatives by algorithmic differentiation
- Introduction to Smooth Manifolds
- Automatic Differentiation Through the Use of Hyper-Dual Numbers for Second Derivatives
- Line Integral Methods for Conservative Problems
- Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
- The MATLAB ODE Suite
- Solving Ordinary Differential Equations I
- An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
- Efficient MATLAB Computations with Sparse and Factored Tensors
- Algorithm 984
- A benchmark of selected algorithmic differentiation tools on some problems in computer vision and machine learning
- A Dynamic Precision Floating-Point Arithmetic Based on the Infinity Computer Framework
- A Study of Mathematical Determination through Bertrand’s Paradox
- Geometric Numerical Integration
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