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Optimization of Adams-type difference formulas in Hilbert space W2(2,1)(0, 1).
- Source :
-
Journal of Computational Analysis & Applications . Jan2024, Vol. 32 Issue 1, p300-319. 20p. - Publication Year :
- 2024
-
Abstract
- In this paper, we consider the problem of constructing new optimal explicit and implicit Adams-type difference formulas for finding an approximate solution to the Cauchy problem for an ordinary differential equation in a Hilbert space. In this work, I minimize the norm of the error functional of the difference formula with respect to the coefficients, we obtain a system of linear algebraic equations for the coefficients of the difference formulas. This system of equations is reduced to a system of equations in convolution and the system of equations is completely solved using a discrete analog of a differential operator d²/dx² - 1. Here we present an algorithm for constructing optimal explicit and implicit difference formulas in a specific Hilbert space. In addition, comparing the Euler method with optimal explicit and implicit difference formulas, numerical experiments are given. Experiments show that the optimal formulas give a good approximation compared to the Euler method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 32
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 175407364