A Fixed-Grid Rdtm-Based Computational Strategy for Nonlinear Partial Differential Equations

Sema Servi; Galip   Oturanç

doi:10.58190/imiens.2025.127

Authors

Sema Servi Department of Computer Engineering, Faculty of Technology, Selçuk University, Konya, Türkiye https://orcid.org/0000-0003-2069-9085
Galip Oturanç Department of Mathematics, Faculty of Science, Karamanoğlu Mehmetbey University, Karaman, Türkiye https://orcid.org/0000-0003-3809-9694

DOI:

https://doi.org/10.58190/imiens.2025.127

Keywords:

Partial Differential Equations, Reduced Differential Transform Method, Intelligent Systems, Klein-Gordon Equation

Abstract

In this study, a fixed-grid version of the Reduced Differential Transform Method (RDTM) is systematically implemented to obtain approximate solutions of linear and nonlinear partial differential equations. In this method, the solution range is divided into equal subregions and the fixed-grid algorithm is integrated into the RDTM framework. This approach provides an efficient and orderly computational process for solving complex partial differential equations. The effectiveness of the proposed method is demonstrated on the homogeneous Klein–Gordon equation (a representative hyperbolic equation) and the nonlinear Klein–Gordon equation, and the obtained approximate solutions are compared with known analytical solutions with high accuracy and consistency. Furthermore, the proposed fixed-grid RDTM (FGS-RDTM) framework offers potential integration with intelligent systems where accurate and efficient numerical solvers are required for modeling, control, and learning in dynamic environments. These results confirm the reliability and practical usefulness of the new method in addressing nonlinear partial differential equations in the context of intelligent computational systems.

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