This paper introduces an accurate greedy-based radial basis function-generated finite difference (RBF-FD) method for solving two-dimensional evolution equations with multi-term tempered kernels. The proposed method combines the flexibility of the RBF-FD approach with the backward Euler (BE) and second-order backward differentiation formula (BDF2) time-stepping schemes. We also use a greedy algorithm to select the collocation points for spatial discretization optimally. This addresses the critical challenge of node placement and enhances the stability and accuracy of the solution. The method offers a robust and flexible framework for modeling complex systems with memory effects and nonlocal interactions. Numerical examples demonstrate the method’s accuracy and efficiency across various domains. Additionally, we present a practical approach for evaluating convergence when the exact solution is unknown, which is essential for real-world applications. The obtained numerical results demonstrate the superiority of the BDF2 over the BE scheme in accuracy and convergence rate, illustrating the effectiveness of the proposed combined spatial and temporal approach.
