RIMNI SPECIAL ISSUE - Analytical Iterative and Transform Techniques for Solving Physical Problems

Deadline Date: 30 June 2026

Analytical solutions play an important role and provide a deeper understanding of the physical solutions of differential equations. Although exact analytical solutions in the closed form functions are very rare, iterative analytical solutions in the form of series and/or transform techniques have proved to be effective in constructing semi-analytical solutions. Since they are complex in nature, these techniques are usually combined with various numerical techniques also. The aim of the special issue is to bring together scientist using common semi- analytical techniques together, to collect high-quality work and provide a dissemination of recent results on the topic.
Perturbation techniques may be considered the oldest and common series type solutions. The limitations of the technique to small parameters lead to many iterative analytical techniques recently. Some of the techniques to avoid such restrictions are the Perturbation Iteration Method, Iteration Perturbation Technique, Homotopy Perturbation Method, Homotopy Analysis Method, Variational Iteration Method, Differential Transform Method, Adomian Decomposition Method, Optimal Homotopy Asymptotic Method, Taylor Matrix Method etc. Variants of the perturbation techniques which do not require small parameter assumptions are also welcome. Solutions of physical problems in any of the iterative analytical methods are within the scope of this special issue.
Another important unified approach to solve differential equations is the Lie Group theory and its restricted form similarity transformations. Usually, the equations are first transformed into a solvable form via the symmetries of the equations. Since the resulting equations are also complex in nature, resort to numerical techniques may be inevitable. Employment of such techniques in search of solutions to the physical problems is welcome.
Solutions of differential equations that do not stem from physical applications are discouraged. Also purely numerical solution techniques without applying some form of analytical techniques are not within the scope of this special issue. As mentioned above, a combination of analytical and numerical techniques in search of solutions of physical problems are within the scope of this special issue.

Deadline Date: 30 June 2026

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