Tau numerical solution of the Volterra-Fredholm Hammerstein integro-differential equations with the Bernstein multi-scaling functions
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@Article{JICS-8-243,
author = {Yadollah Ordokhani Solmaz Moosavi and Mohsen Shahrezaee},
title = {Tau numerical solution of the Volterra-Fredholm Hammerstein integro-differential equations with the Bernstein multi-scaling functions},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {8},
number = {4},
pages = {243--255},
abstract = { This paper involves the development of the Tau method with Bernstein multi-scaling (BMS)
functions basis for the numerical solution of the Volterra-Fredholm Hammerstein integro-differential
equations (VFHIDEs). For this purpose at the beginning we define BMS functions and express briefly some
properties of BMS functions and after function approximation by using BMS functions, will be presented.
Then, the operator matrix representation for the differential and integral parts seeming in the equation using
the operational Tau method base on BMS functions basis, will be displaced. The operational Tau method
transforms the differential and integration parts of the desired VFHIDEs to some operational matrices. In fact,
this method reduces VFHIDEs to a system of algebraic equations. Numerical examples demonstrate the
validity and applicability of the proposed method with BMS functions basis.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22600.html}
}
TY - JOUR
T1 - Tau numerical solution of the Volterra-Fredholm Hammerstein integro-differential equations with the Bernstein multi-scaling functions
AU - Yadollah Ordokhani Solmaz Moosavi and Mohsen Shahrezaee
JO - Journal of Information and Computing Science
VL - 4
SP - 243
EP - 255
PY - 2024
DA - 2024/01
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22600.html
KW - Bernstein multi-scaling functions , Operational Tau method , Hammerstein integro-differential
equation, Algebraic equation, Fredholm, Volterra.
AB - This paper involves the development of the Tau method with Bernstein multi-scaling (BMS)
functions basis for the numerical solution of the Volterra-Fredholm Hammerstein integro-differential
equations (VFHIDEs). For this purpose at the beginning we define BMS functions and express briefly some
properties of BMS functions and after function approximation by using BMS functions, will be presented.
Then, the operator matrix representation for the differential and integral parts seeming in the equation using
the operational Tau method base on BMS functions basis, will be displaced. The operational Tau method
transforms the differential and integration parts of the desired VFHIDEs to some operational matrices. In fact,
this method reduces VFHIDEs to a system of algebraic equations. Numerical examples demonstrate the
validity and applicability of the proposed method with BMS functions basis.
Yadollah Ordokhani Solmaz Moosavi and Mohsen Shahrezaee. (2024). Tau numerical solution of the Volterra-Fredholm Hammerstein integro-differential equations with the Bernstein multi-scaling functions.
Journal of Information and Computing Science. 8 (4).
243-255.
doi:
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