In this paper, we introduce a meshless method based on the Partition of Unity (PU) interpolation technique to solve two-dimensional coupled Klein-Gordon-Schr{\"o}dinger (KGS) equations on scattered data within arbitrary domains. The approach begins with a time-discrete scheme derived from a finite difference approximation of the time derivative, followed by the application of the PU method to discretize the spatial derivatives. The PU technique combines local approximations using radial basis functions with compactly supported weight functions to ensure efficient and accurate interpolation over irregular node distributions. To handle the nonlinearity inherent in the KGS system, a predictor-corrector scheme is employed. Numerical experiments demonstrate the effectiveness of the PU-based method, with results compared against analytical solutions and stability analyses confirming its accuracy and computational efficiency for complex geometries.
Jafarabadi,A . (2025). A Partition of Unity Meshless Method for Solving Two-Dimensional Coupled Klein-Gordon-Schrödinger Equations. Journal of Applied Mathematics & Data Analytics, 1(1), 82-100. doi: 10.311581/JAMDA.2509.1010.1.1.6
MLA
Jafarabadi,A . "A Partition of Unity Meshless Method for Solving Two-Dimensional Coupled Klein-Gordon-Schrödinger Equations", Journal of Applied Mathematics & Data Analytics, 1, 1, 2025, 82-100. doi: 10.311581/JAMDA.2509.1010.1.1.6
HARVARD
Jafarabadi A. (2025). 'A Partition of Unity Meshless Method for Solving Two-Dimensional Coupled Klein-Gordon-Schrödinger Equations', Journal of Applied Mathematics & Data Analytics, 1(1), pp. 82-100. doi: 10.311581/JAMDA.2509.1010.1.1.6
CHICAGO
A Jafarabadi, "A Partition of Unity Meshless Method for Solving Two-Dimensional Coupled Klein-Gordon-Schrödinger Equations," Journal of Applied Mathematics & Data Analytics, 1 1 (2025): 82-100, doi: 10.311581/JAMDA.2509.1010.1.1.6
VANCOUVER
Jafarabadi A. A Partition of Unity Meshless Method for Solving Two-Dimensional Coupled Klein-Gordon-Schrödinger Equations. JAMDA. 2025;1(1):82-100. doi: 10.311581/JAMDA.2509.1010.1.1.6
