In this work, one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) coupled damped Schrödinger system is solved numerically. A strong-form local meshless approach established on radial basis function-finite difference (RBF-FD) method for spatial approximation is developed. Polyharmonic splines are used as radial basis function with augmented polynomials. The use of the polyharmonic splines saves us from choosing an optimum shape parameter which is not a simple task for infinitely smooth RBFs such as multiquadrics or Gaussians. For time discretization classical fourth-order Runge Kutta method is utilized. $L_{\infty }$ error norm and conserved quantities are computed to indicate performance of the proposed method. Stability of the proposed method is examined numerically. Some computer codes are devised in Julia programming language for obtaining numerical results. Acquired numerical results and their comparison with other studies available in literature such as cubic B-spline Galerkin method and direct meshless local Petrov–Galerkin (DMLPG) method endorse the performance and reliability of the proposed method.

在这项工作中，对一维 (1D)、二维 (2D) 和三维 (3D) 耦合阻尼薛定谔系统进行了数值求解。开发了一种基于径向基函数有限差分 (RBF-FD) 方法的强形式局部无网格方法，用于空间逼近。多谐样条用作具有增广多项式的径向基函数。多谐波样条的使用使我们不必选择最佳形状参数，这对于无限平滑的 RBF（如多二次曲面或高斯函数）来说不是一项简单的任务。对于时间离散，使用经典的四阶 Runge Kutta 方法。${升}_{\infty }$计算误差范数和守恒量以表明所提出方法的性能。所提出的方法的稳定性进行了数值检验。一些计算机代码是用 Julia 编程语言设计的，用于获得数值结果。获得的数值结果及其与文献中其他研究的比较，如三次 B 样条伽辽金方法和直接无网格局部彼得罗夫-伽辽金 (DMLPG) 方法，证实了所提出方法的性能和可靠性。