Convergence and Stability of Modified Adomian Decomposition Method
Emad Az-Zo'bi
Broschiertes Buch

Convergence and Stability of Modified Adomian Decomposition Method

Theory and Computations for Mixed Hyperbolic-Elliptic Systems of Conservation Laws

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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.