带三次项的非线性四阶Schrdinger方程的一个局部能量守恒格式

A LOCAL ENERGY CONSERVATIVE SCHEME FOR THE FOURTH-ORDER SCHRDINGER EQUATION WITH CUBIC NONLINEAR TERM

本文构造了带三次项的非线性四阶Schodinger方程的一个局部能量守恒格式.证明了该格式是线性稳定的,且能保持离散的整体能量守恒律及离散的电荷守恒律.最后通过数值算例验证了理论结果的正确性.

In this paper, a local energy conservative scheme is constructed to solve the fourth-order SchrSdinger equation with cubic nonlinear term. We prove that the scheme is linear stable and preserves the discrete global energy and discrete charge. Finally, the correctness of the theoretical results is demonstrated by the numerical examples.