The Nonlinearity effect on the morphology, stability, and regularity of the diffusion, dispersion, and convection term in the analytic solutions of certain frontier nonlinear partial differential equations.

Baiju S

doi:10.36948/ijfmr.2026.v08i01.66397

The Nonlinearity effect on the morphology, stability, and regularity of the diffusion, dispersion, and convection term in the analytic solutions of certain frontier nonlinear partial differential equations.

Author(s)	Dr. Baiju S
Country	India
Abstract	In the paper, the Laplace-Adomian Decomposition Algorithm is used to solve several frontier nonlinear partial differential equations analytically. For the analytic or semi-analytic solution of nonlinear partial, integral, and integro-differential equations as well as the system of such equations, the author modified and extended the Laplace Adomian Decomposition Method to the Laplace Adomian Decomposition Algorithm and developed it for boundary value problems as the Shooting-Type Laplace-Adomian Decomposition Algorithm. The author has authored a few related papers, which are included in the bibliography. Analytical solutions are crucial because they provide a physical insight of the phenomenon and can be applied directly or modified appropriately to make them applicable to other phenomena. To obtain an analytic solution, the method does not require linearization, discretisation, perturbation, or initial term guess. Additionally, this approach has certain drawbacks when dealing with singular situations, fractional nonlinearity, trigonometric nonlinearity, and at the poles. When compared to other analytical techniques, the method's convergence is high in differential, polynomial, and exponential cases. Convection, diffusion, and dispersion features of fluid dynamics—particularly gas dynamics, which is the movement of air, gases, or motion of objects, bodies, or materials through the air and its consequences on physical systems—were addressed in the paper. The efficiency, precision, and significance of solving nonlinear equations with initial and boundary conditions are highlighted in this paper.
Keywords	Nonlinear partial differential equations, domain of existence, Adomian polynomials, Dynamic equations, Advection and K(2, 2) equation, Shooting-Type Laplace-Adomian Decomposition Algorithm.
Field	Mathematics > Maths + Physics
Published In	Volume 8, Issue 1, January-February 2026
Published On	2026-01-12
DOI	https://doi.org/10.36948/ijfmr.2026.v08i01.66397

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The Nonlinearity effect on the morphology, stability, and regularity of the diffusion, dispersion, and convection term in the analytic solutions of certain frontier nonlinear partial differential equations.

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