Huda O. Bakodah

Solving a class of partial differential equations with different types of boundary conditions by using a generalized inverse operator: decomposition method

In this paper, a class of partial differential equations has been studied by the Adomian decomposition method. A generalized inverse operator has been developed to solving various partial differential equations with different types of boundary conditions (Dirichlet, Neumann, and mixed). Several examples in physics and fluid mechanics have been analyzed by the present approach, where a remarkable accuracy has been achieved.

APPROXIMATE ANALYTICAL SOLUTION FOR ONE DIMENSIONAL PROBLEMS OF THERMOELASTICITY WITH DIRICHLET CONDITION

This paper presents the solution of the initial boundary- value problem for the system of one-dimensional thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method.