Numerical approximation of 1D and 2D non-linear Schrödinger equations by implementing modified cubic Hyperbolic B-spline based DQM

Abstract

In present study, Modified Cubic Hyperbolic B-spline Differential Quadrature Method is constructed for getting the numerical approximations of 1D and 2D non-linear Schrödinger equations. Modified cubic Hyperbolic B-spline is implemented as basis function to compute the required weighting coefficients regarding DQM. Thereafter, by spatial discretization, obtained system of ordinary differential equations is obtained which is tackled using Strong Stability Preserving-Runge–Kutta 43 scheme. Accuracy of the proposed scheme is tested by comparing the exact and numerical approximations. L2and L∞errors are computed for different parameters.

Keywords

• 1D and 2D non-linear Schrödinger equations
• Hyperbolic B-spline
• Differential Quadrature Method
• SSP-RK43 scheme