Optimal coefficients of an implicit difference formula in the Hilbert space

Many real-world problems, when formulated mathematically, lead to differential equations. We can encounter a number of these equations in the study of such phenomena as the motion of an object moving in a straight line, the decay of radioactive material, population growth, and the cooling of a heate...

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Bibliographic Details
Main Authors: Shadimetov, Kholmat, Karimov, Rozik
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Differential equations
Formulas (mathematics)
Hilbert space
Independent variables
Numerical analysis
Numerical methods
Object motion
Ordinary differential equations
Population growth
Radioactive materials
Straight lines
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Summary:Many real-world problems, when formulated mathematically, lead to differential equations. We can encounter a number of these equations in the study of such phenomena as the motion of an object moving in a straight line, the decay of radioactive material, population growth, and the cooling of a heated object placed in an environment with a lower temperature. Numerical methods for the approximate solution of Initial Value Problems for ordinary differential equations serve to determine and approximate the functions representing the solution of these problems. In these days it is of great interest to consider the so-called discrete methods, i.e. methods that determine the solution for discrete values of the independent variable. Currently, discrete methods are most commonly used. One of the discrete method is the difference formula for numerically solving the Initial Value Problems. The difference method is a universally applicable numerical method for solving differential equations. The present work is devoted finding optimal coefficients of an implicit difference formula in the Hilbert space.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0200065