Geometric Sinc Method to Solve Non‐Newtonian Integro Differential Equations

ABSTRACT In this work, we introduce a novel numerical technique for solving geometric differential equations, termed the geometric sinc method (G‐Sinc method). This method constructs highly accurate approximations by leveraging both the geometric structure of the underlying problem and the analytical strength of the sinc function. To accommodate the geometric features of the solution domain, we define a modified G‐Sinc basis and develop a corresponding computational framework. Several illustrative examples are presented to demonstrate the method's accuracy and efficiency. Comparative results with known exact solutions and conventional numerical approaches show that the G‐Sinc method offers several key advantages: improved accuracy with fewer grid points, better handling of boundary singularities, and enhanced stability for complex geometries. These results indicate that the G‐Sinc method is a powerful and promising tool for solving a broad class of geometric differential equations with superior precision and computational efficiency.