S L Shaikh
Integral Transforms; Partial Differential Equations
|PUBLISHED DATE||September, 2018|
|PUBLISHER||The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications.|
In this paper we have derived Sadik transform of the partial derivatives of a function of two variables. We have demonstrated the applicability of the Sadik transform by solving some examples of partial differential equations. We have verified solutions of partial differential equations by Sadik transform with the Laplace transform and the Sumudu transform.
There are a lot of methods to solve partial differential equations, but for linear partial differential equations the most powerful method is an integral transformation method. Laplace transform is the most effective tool to solve some kinds of ordinary and partial differential equations. Actually an electric engineer Oliver Heaviside made Laplace transform popular by developing its operational calculus. After Laplace transform, in 1993 again an electrical engineer Watugula in (Watugula 1993) proposed a new integral transform named the Sumudu transform and used it for solving problems in control engineering, it is similar to the Laplace transform having the preservation property of unit and change of scale. After that, T. Elzaki (Tariff 2011) introduced a new integral transform named Elzaki transform and applied it for solving partial differential equations, Shaikh Sadikali has been applied Elzaki transform for solving integral equations of convolution type see in (Shaikh 2011). Likewise many integral transforms have been proposed which are similar to the Laplace transform, and each new transform claimed its own superiority over the Laplace transform. In this paper we considered a new integral transform named the Sadik transform (Shaikh 2018 & 2018). It is similar to the Laplace transform but the Laplace transform, the Sumudu transform, Elzaki transform and all integral transforms with kernel of an exponential type are particular cases of the Sadik transform. Due to the very general and unified nature of the Sadik transform, we can transport a problem of partial differential equations into the known transformation technique which is available in the literature through the Sadik transform.
|ISSN||Print: 2278-9561, Online: 2278-957X|
Sadik transform has been successfully applied to solve partial differential equations in a simple manner.