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Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
- Source :
- Demonstratio Mathematica, Vol 54, Iss 1, Pp 11-24 (2021)
- Publication Year :
- 2021
- Publisher :
- Walter de Gruyter GmbH, 2021.
-
Abstract
- The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.
- Subjects :
- convergence
General Mathematics
homotopy analysis method
65r20
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Fuzzy logic
Volterra integral equation
symbols.namesake
Nonlinear system
error estimation
Convergence (routing)
QA1-939
0202 electrical engineering, electronic engineering, information engineering
symbols
45g10
Applied mathematics
two-dimensional nonlinear fuzzy volterra integral equation
020201 artificial intelligence & image processing
0101 mathematics
41a25
Mathematics
Homotopy analysis method
Subjects
Details
- ISSN :
- 23914661
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- Demonstratio Mathematica
- Accession number :
- edsair.doi.dedup.....777ecf6b8ad622f53f0c64cf73302283