arrow
Volume 8, Issue 4
Tau numerical solution of the Volterra-Fredholm Hammerstein integro-differential equations with the Bernstein multi-scaling functions

Yadollah Ordokhani Solmaz Moosavi and Mohsen Shahrezaee

J. Info. Comput. Sci. , 8 (2013), pp. 243-255.

Export citation
  • 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.
  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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:
Copy to clipboard
The citation has been copied to your clipboard