Analytical Solutions of Nonlinear Partial Differential Equations Using the Double Sawi–Adomian Decomposition Method
Year: 2026
Type: article
Abstract: A double Sawi–Adomian decomposition framework is developed for nonlinear initial‐value problems with one space and one time variable. The double transform converts the time derivative and the prescribed data into a Volterra integral equation, whereas Adomian polynomials organize the nonlinear term. In contrast with earlier transform–decomposition studies that mainly report formal series, the present formulation includes a contraction condition for existence and uniqueness, a convergence criterion for the decomposition series, and both a priori and residual‐based truncation bounds. A second‐order nonlinear equation and the inviscid Burgers equation are examined. Their decomposition components reproduce the Taylor expansions of tanh(2 ξ τ ) and ξ /(1 + τ ), respectively. Numerical error tables show the effect of the truncation order and also expose the finite radius of convergence in the Burgers example. Thus, the contribution is a certified double‐Sawi formulation rather than a claim that changing the transform alone alters the underlying Adomian approximation.
Source: Journal of Applied Mathematics
DOI: 10.1155/jama/2272559
Authors: Monther Al-Momani, Baha′ Abughazaleh
Institutions: Amman Arab University, Isra University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,130
OpenAlex ID: W7220866646