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Numerical analysis of block-by-block method for a class of fractional relaxation-oscillation equations.
- Source :
-
Applied Numerical Mathematics . Jun2022, Vol. 176, p38-55. 18p. - Publication Year :
- 2022
-
Abstract
- Fractional relaxation-oscillation equation (FROE) is an important physical model describing oscillators. Its numerical solution method has profound theoretical significance and application value. In this paper, we use a non-singularity kernel Volterra integral equation of block-by-block method and construct a block-by-block numerical scheme based on Lagrange basis function interpolation. The analysis proves the stability and convergence of the block-by-block method. Error analysis shows that the convergence order is at least 4 which significantly improves calculation accuracy. Through the error comparison, the error of block-by-block method in this paper is significantly lower than that prediction-correction(P-C) method, which overcomes the shortcomings of the existing methods of low accuracy in solving FROE. Both theoretical analysis and numerical experiments show the high accuracy and effectiveness of the block-by-block numerical scheme, which shows that the method in this paper is efficient and feasible to solve the FROE. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NUMERICAL analysis
*VOLTERRA equations
*EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 176
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 155960700
- Full Text :
- https://doi.org/10.1016/j.apnum.2022.02.008