Compact and efficient conservative schemes for coupled nonlinear <scp>S</scp>chrödinger equations

Abstract

In the manuscript, we present several numerical schemes to approximate the coupled nonlinear Schrödinger equations. Three of them are high‐order compact and conservative, and the other two are noncompact but conservative. After some numerical analysis, we can find that the schemes are uniquely solvable and convergent. All of them are conservative and stable. By calculating the complexity, we can find that the compact schemes have the same computational cost with the noncompact ones. Numerical illustrations support our analysis. They verify that compact schemes are more efficient than noncompact ones from computation cost and accuracy. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1814–1843, 2015