A note on comparison between laplace and sumudu transfoms
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CitationKılıçman, A., Eltayeb, H. ve Bin Mohd Atan, K. A. (2009). A note on comparison between laplace and sumudu transfoms. Maltepe Üniversitesi. s. 66.
In the literature there are several works on the theory and applications of integral transforms by changing the kernel in the integral transform one can have several different transform such as Laplace, Fourier, Mellin, Hankel, to name a few, but very little on the power series transformation such as Sumudu transform, probably because it is little known, and not widely used yet. Recently, the Sumudu transform was proposed originally by Watugala see  and defined by F (u) = 1 u Z ∞ 0 e −( t u ) f(t)dt, (1) over the set of the functions A = ½ f(t) | ∃M, τ1, τ2 > 0, |f(t)| < Me t τj , if t ∈ (−1)j × [0, ∞) ¾ where f(t) is a function which can be expressed as a convergent infinite series, see  and similarly the double Sumudu transform is defined by F (v, u) = S2 [f(t, x); (v, u)] = 1 uv Z ∞ 0 Z ∞ 0 e −( t v + x u ) f(t, x) dt dx, (2) see , or . Further this new integral transform generalized and applied by Kılı¸cman and Eltayeb to the linear second order partial differential equations with non-constant coefficients as well as to generalized functions, for more details see . In this paper, we discuss existence of the double Sumudu transform and established some relationship between Laplace and Sumudu transforms. Further, we apply two transforms to solve the linear ordinary differential equations with non constant coefficients, in special case, we provide some examples related to the second order differential equations having non-constant coefficients.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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