论文信息 - On Double Sumudu Transform and Double Laplace Transform

On Double Sumudu Transform and Double Laplace Transform

In this study, first of all, we consider wave equations with constant coefficients. By using convolution we then produce a new equation with variable coefficients. Finally, we apply two techniques: double Laplace transform and double Sumudu transform to solve the new wave equation with non-constant coefficients and establish a relationship between double Sumudu transform and double Laplace transform.

Adem Kilicman | Hassan Eltayeb | A. Kılıçman | H. Eltayeb

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

[2] 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..

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

[4] SYSTEMS OF MULTI-DIMENSIONAL LAPLACE TRANSFORMS AND A HEAT EQUATION , 2001 .

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

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

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

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

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

[10] H. Bateman. Partial Differential Equations of Mathematical Physics , 1932 .

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