Methods for solving the initial value problem with a two-sided estimate of the local error

Pelekh, Yaroslav; Kunynets, Andrii; Beregova, Halyna; Magerovska, Tatiana

doi:10.15407/fmmit2021.33.088

Fìz.-mat. model. ìnf. tehnol.

2021

DOI: 10.15407/fmmit2021.33.088

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Methods for solving the initial value problem with a two-sided estimate of the local error

Yaroslav Pelekh

Andrii Kunynets

Halyna Beregova

et al.

Abstract: Numerical methods for solving the initial value problem for ordinary differential equations are proposed. Embedded methods of order of accuracy 2(1), 3(2) and 4(3) are constructed. To estimate the local error, two-sided calculation formulas were used, which give estimates of the main terms of the error without additional calculations of the right-hand side of the differential equation, which favorably distinguishes them from traditional two-sided methods of the Runge- Kutta type.

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“…Approximation by rational fractions has a number of advantages over other types of approximation [5,6]. In particular, rational fractions can provide:…”

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confidence: 99%

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

Izonin

2023

mcm-tech

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Intelligence analysis of tabular datasets in the field of biomedical engineering is a complex task. This is explained both by the multidimensional datasets and the complex relationships between the components of the set, and by the high price of the error in the prediction. The task becomes more difficult in the case of limited data for training, which often occurs in this field. This is due to the enormous time, material, or human resources required to collect enough data to implement training procedures with classical machine learning tools. This paper presents a new approach to solving this task. The author has developed a new ensemble method for the regression model parameters adjustments (direct approach) with the possibility of cyclically increasing the accuracy of intellectual analysis of short datasets. The basis of the method is the use of the rational fraction and two machine learning algorithms for its parametric identification. Modeling of the method's efficiency on a real-world short set of data from the field of biomedical engineering demonstrated the high accuracy of the developed method's operation. In particular, the prediction accuracy of the General Regression Neural Network was increased by more than 14% (based on the coefficient of determination. That is why the developed method can be used to solve various applied biomedical engineering tasks in the case of the need to analyze small amounts of data

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“…Approximation by rational fractions has a number of advantages over other types of approximation [5,6]. In particular, rational fractions can provide:…”

mentioning

confidence: 99%

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

Izonin

2023

mcm-tech

View full text Add to dashboard Cite

show abstract

Two-Sided Methods for Solving Initial Value Problem for Nonlinear Integro-Differential Equations

Pelekh¹,

Kunynets²,

Pelekh³

2022

JNAM

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Using the continued fractions and the method of constructing Runge-Kutta methods, numerical methods for solving the Cauchy problem for nonlinear Volterra non-linear integrodifferential equations are proposed. With appropriate values of the parameters, one can obtain an approximation to the exact solution of the first and second order of accuracy. We found a set of parameters for which we obtain two-sided calculation formulas, which at each step of integration allow to obtain the upper and lower approximations of the exact solution.

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Methods for solving the initial value problem with a two-sided estimate of the local error

Cited by 2 publications

References 1 publication

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

An Ensemble Method for the Regression Model Parameter Adjustments: Direct Approach

Two-Sided Methods for Solving Initial Value Problem for Nonlinear Integro-Differential Equations

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