Sumudu transform
From HandWiki
Short description: Integral transform introduced in 1990
The Sumudu transform is an integral transform introduced in 1990 by G K Watagala.[1][2][3][4] It is defined as the set as [5][6][7]
[math]\displaystyle{ S = \{f(t) : \ni M, p ,q\gt 0 , |f(t)|= M \exp(1/u) \} }[/math]
where [math]\displaystyle{ p \leq u \leq q }[/math]
and the Sumudu transform is defined as
[math]\displaystyle{ A[f(t)]= \frac 1 u \int_0^\infty f(t) \exp\left(\frac1u\right) \, dt. }[/math]
Relationship with other transforms
Sumudu transform is 1/u Laplace transform [math]\displaystyle{ S[f(t)](u)=\frac{1}{u} L[f(t)](\frac{1}{u}) }[/math] And with u2 Elzaki transform [math]\displaystyle{ S[f(t)](u)= u^2 E[f(t)](u) }[/math]
References
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- ↑ Watugala, G. K. (January 1993). "Sumudu transform: a new integral transform to solve differential equations and control engineering problems". International Journal of Mathematical Education in Science and Technology 24 (1): 35–43. doi:10.1080/0020739930240105. ISSN 0020-739X. http://www.tandfonline.com/doi/abs/10.1080/0020739930240105.
- ↑ "Error: no
|title=specified when using {{Cite web}}". https://scholar.google.co.in/scholar_url?url=https://downloads.hindawi.com/archive/2006/091083.pdf&hl=en&sa=X&ei=BGirZdzlKfKc6rQPgIKU6As&scisig=AFWwaeYEO-3HYLsYwW2gbhf7ehJl&oi=scholarr. - ↑ Asiru, Muniru Aderemi (May 2002). "Further properties of the Sumudu transform and its applications" (in en). International Journal of Mathematical Education in Science and Technology 33 (3): 441–449. doi:10.1080/002073902760047940. ISSN 0020-739X. http://www.tandfonline.com/doi/abs/10.1080/002073902760047940.
- ↑ Zhang, Jun; Shen, Fangyang (2018). "Sumudu Transform for Automatic Mathematical Proof and Identity Generation". in Latifi, Shahram (in en). Information Technology - New Generations. Advances in Intelligent Systems and Computing. 558. Cham: Springer International Publishing. pp. 677–683. doi:10.1007/978-3-319-54978-1_85. ISBN 978-3-319-54978-1. https://link.springer.com/chapter/10.1007/978-3-319-54978-1_85.
- ↑ Kılıcman, A.; Gadain, H. E. (2010-06-01). "On the applications of Laplace and Sumudu transforms". Journal of the Franklin Institute 347 (5): 848–862. doi:10.1016/j.jfranklin.2010.03.008. ISSN 0016-0032. https://www.sciencedirect.com/science/article/pii/S0016003210000785.
- ↑ Watugala, G. K. (January 1993). "Sumudu transform: a new integral transform to solve differential equations and control engineering problems" (in en). International Journal of Mathematical Education in Science and Technology 24 (1): 35–43. doi:10.1080/0020739930240105. ISSN 0020-739X. http://www.tandfonline.com/doi/abs/10.1080/0020739930240105.
- ↑ Kapoor, Mamta (June 15, 2023). "Sumudu Transform for Time Fractional Physical Models an Analytical Aspect" (in en). Journal of Applied Analysis & Computation 13 (3): 1255–1273. doi:10.11948/20220096. ISSN 2156-907X. http://jaac.xml-journal.cn/en/article/doi/10.11948/20220096.
