Hassan Eltayeb

A new integral transform and associated distributions

In this paper, we generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

On Sumudu Transform and System of Differential Equations

The regular system of differential equations with convolution terms solved by Sumudu transform.

A note on solutions of wave, Laplace's and heat equations with convolution terms by using a double Laplace transform

In this study we consider general linear second-order partial differential equations and we solve three fundamental equations by replacing the non-homogeneous terms with double convolution functions and data by a single convolution.

A note on defining singular integral as distribution and partial differential equations with convolution term

In this study first we consider the singular integrals as generalized functions in two dimensions and then we solve the non-homogeneous wave equation with convolutional term by using the generalized functions as boundary conditions.

A note on the classifications of hyperbolic and elliptic equations with polynomial coefficients

In this work we consider the hyperbolic and elliptic partial differential equations with constant coefficients; then by using double convolutions we produce new equations with polynomial coefficients and classify the new equations. It is shown that the classifications of hyperbolic and elliptic equations with non-constant coefficients are similar to those of the original equations; that is, the equations are invariant under double convolutions.

On a New Integral Transform and Differential Equations

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, it was proved that Sumudu transform has very special and useful properties. In this paper we study this interesting integral transform and its efficiency in solving the linear ordinary differential equations with constant and nonconstant coefficients as well as system of differential equations.

A Note on Double Laplace Transform and Telegraphic Equations

Double Laplace transform is applied to solve general linear telegraph and partial integrodifferential equations. The scheme is tested through some examples, and the results demonstrate reliability and efficiency of the proposed method.

Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

Application of Sumudu Decomposition Method to Solve Nonlinear System Volterra Integrodifferential Equations

We develop a method to obtain approximate solutions for nonlinear systems of Volterra integrodifferential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled Volterra integrodifferential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples and results of the present technique have close agreement with approximate solutions which were obtained with the help of Adomian decomposition method (ADM).

Exact Evaluation of Infinite Series Using Double Laplace Transform Technique

Double Laplace transform method was applied to evaluate the exact value of double infinite series. Further we generalize the current existing methods and provide some examples to illustrate and verify that the present method is a more general technique.