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1 year ago in Applied Mathematics , Complex Analysis By Niranjan Singh

Can Adomian decomposition be applied to nonlinear equations in complex space?

In my work on nonlinear dynamical systems, I often encounter equations where the solution is analytic in the complex plane. I’m trying to see if Adomian’s method, which is powerful for real nonlinearities, retains its convergence and utility when we extend the problem into complex space, or if unique analytical hurdles emerge.

Nonlinear Dynamics AdomianDecomposition

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By Usha K Answered 1 year ago

I have applied Adomian's method to both real and complex nonlinear systems in my research. While the formalism extends naturally to complex space you treat the independent variable as complex the primary challenges shift. Convergence is the critical issue. The series solution must be analytic within your domain of interest, and the radius of convergence can be severely limited by singularities. I would recommend a preliminary analysis of the nonlinearity's behavior in the complex plane before committing to the decomposition. Pairing it with Padé approximants can often help extend usability.

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Can Adomian decomposition be applied to nonlinear equations in complex space?

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