On the applications of Laplace and Sumudu transforms

In this paper, we study the properties of Sumudu transform and relationship between Laplace and Sumudu transforms. Further, we also provide an example of the double Sumudu transform in order to solve the wave equation in one dimension which is having singularity at initial conditions.

[1]  P. Zweifel.  A Review of: “Partial differential equations of mathematical physics, Tyn Myint-U, (North-Holland, 1980). $24.50 USA” , 1981 .

[2]  I︠u︡. A Brychkov.  Multidimensional integral transformations , 1992 .

[3]  C. Constanda.  Solution Techniques for Elementary Partial Differential Equations , 2002 .

[4]  Jun Zhang,et al.  A Sumudu based algorithm for solving differential equations , 2007, Comput. Sci. J. Moldova.

[5]  Dean G. Duffy,et al.  Transform Methods for Solving Partial Differential Equations , 2004 .

[6]  T. Higgins,et al.  The solution of boundary value problems by multiple Laplace transformations , 1951 .

[7]  Adem Kilicman,et al.  On Sumudu Transform and System of Differential Equations , 2010 .

[8]  APPLICATIONS OF SUMUDU TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS , 2010 .

[9]  G. K. Watugala,et al.  Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems , 1992 .

[10]  Jean M. Tchuenche,et al.  AN APPLICATION OF THE DOUBLE SUMUDU TRANSFORM , 2007 .

[11]  Sunethra Weerakoon,et al.  Application of Sumudu transform to partial differential equations , 1994 .

[12]  Hassan Eltayeb,et al.  A note on solutions of wave, Laplace's and heat equations with convolution terms by using a double Laplace transform , 2008, Appl. Math. Lett..

[13]  Hassan Eltayeb,et al.  A note on defining singular integral as distribution and partial differential equations with convolution term , 2009, Math. Comput. Model..

[14]  Adem Kilicman,et al.  On Double Sumudu Transform and Double Laplace Transform , 2010 .

[15]  Adem Kilicman,et al.  A new integral transform and associated distributions , 2010 .

[16]  A. Kılıçman,et al.  An application of double Laplace transform and double Sumudu transform , 2009 .

[17]  Muniru A. Asiru,et al.  Further properties of the Sumudu transform and its applications , 2002 .

[18]  Hassan Eltayeb,et al.  A note on the classifications of hyperbolic and elliptic equations with polynomial coefficients , 2008, Appl. Math. Lett..