<p>Numerical methods such as the finite element and finite difference approaches have undergone significant development and refinement over time, enabling the solution of complex engineering and physical systems. However, like many scientific fields today, these methods still grapple with unresolved ambiguities, particularly concerning the mesh and its impact on performance. It is precisely to address these limitations that meshless methods have emerged. With the introduction of meshless methods, a wide range of engineering phenomena have been successfully modeled. While these methods themselves present challenges that necessitate further research and development, they have successfully mitigated some of the weaknesses inherent in the mesh-based nature of traditional numerical methods. This research focuses on a comparative analysis of the local and global approaches within the Multiquadric (MQ) meshless method and presents a new idea for modeling with a local approach. The MQ method, due to its fully populated coefficient matrix and its susceptibility to becoming increasingly ill-conditioned, typically exhibits high sensitivity to shape parameters and can produce unstable results. However, by restricting the Gaussian points associated with computational points, the coefficient matrix becomes sparsely populated, significantly reducing the condition number and leading to more stable solutions. To investigate that, six examples representing common mathematical and engineering problems were modeled using both approaches. Employing the local approach in solving one-dimensional problems yields significant improvements in reducing the condition number of the coefficient matrix. Nevertheless, in two-dimensional problems, the effectiveness of this approach depends on the geometric complexity and the solution gradients. Moreover, it employs a specific mechanism to construct a single function that represents the entire domain.</p>