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A kernel derivative free SPH method
Results in Applied Mathematics, 2023 Based on smooth particle hydrodynamics (SPH) method, this paper proposes the concept of kernel function moment and studies its properties, and puts forward the KDF-SPH (Kernel Derivative Free SPH: KDF-SPH) method.
Dongyan Feng, Rahmatjan Imin
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Basin attractors for derivative-free methods to find simple roots of nonlinear equations
Journal of Numerical Analysis and Approximation Theory, 2020 Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference.
Beny Neta
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A derivative-free optimisation method for global ocean biogeochemical models [PDF]
Geoscientific Model Development, 2022 The skill of global ocean biogeochemical models, and the earth system models in which they are embedded, can be improved by systematic calibration of the parameter values against observations. However, such tuning is seldom undertaken as these models are
S. Oliver +4 more
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Three-Step Derivative-Free Method of Order Six
Foundations, 2023 Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute.
Sunil Kumar +3 more
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A New Derivative-Free Method to Solve Nonlinear Equations
Mathematics, 2021 A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated.
Beny Neta
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A derivative-free Gauss–Newton method [PDF]
Mathematical Programming Computation, 2019 We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the objective, which is then used within a trust-region framework to give a globally-convergent algorithm requiring $O(ε^{-2})
Roberts, L, Cartis, C
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Nonlinear fitting of multi-compartmental data using Hooke and Jeeves direct search method
Open Physics, 2021 Compartmental modelling refers to modelling the transport of substances in a system consisting of multiple compartments, which is characterized by the transfer rates among the relevant compartments.
Beni Mehrdad Shahmohammadi, Yu Kwan Ngok
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Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations
European Journal of Mathematical Analysis, 2023 In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution.
Sunil Kumar +3 more
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Derivative-free optimization methods [PDF]
Acta Numerica, 2019 In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization.
Larson, Jeffrey +2 more
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Derivative free iterative simultaneous method for finding distinct roots of polynomial equation
Alexandria Engineering Journal, 2020 In this article, we present a new derivative free simultaneous method for determining in particular all the distinct roots of polynomial equation. A modification in Weierstrass correction is used to construct tenth order derivative free simultaneous ...
Nazir Ahmad Mir +4 more
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