Convergence and Stability of Modified Adomian Decomposition Method - Az-Zo'bi, Emad
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Adomian decomposition procedure is developed for systems of balance laws (conservation laws with source term). A new formula of Adomian polynomials is introduced. Based on this new formula and using the Banach fixed point theorem, we prove the convergence and stability of a new modification. We show that our modification is stable in several cases. Our method is powerful and efficient that gives approximations of higher accuracy and closed form solutions if existing. The analysis will be illustrated by several systems, like Van der Waals equations in fluid dynamics.

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Produktbeschreibung
Adomian decomposition procedure is developed for systems of balance laws (conservation laws with source term). A new formula of Adomian polynomials is introduced. Based on this new formula and using the Banach fixed point theorem, we prove the convergence and stability of a new modification. We show that our modification is stable in several cases. Our method is powerful and efficient that gives approximations of higher accuracy and closed form solutions if existing. The analysis will be illustrated by several systems, like Van der Waals equations in fluid dynamics.
Autorenporträt
Emad Az-Zo'b was born in Jordan in 1980. Received his PhD degree in Mathematics - Applied Mathematical Analysis specialization - from the University of Jordan in 2011. Made some research on the existence and uniqueness of the solution to some physical models.