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math.NA2022★ 2 cited
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine--Gordon equation
Yue Feng, Katharina Schratz
We establish the improved uniform error bounds on a Lawson-type exponential integrator Fourier pseudospectral (LEI-FP) method for the long-time dynamics of sine-Gordon equation whe…
math.NA2022★ 2 cited
Regularized numerical methods for the nonlinear Schrödinger equation with singular nonlinearity
Weizhu Bao, Yue Feng, Ying Ma
We present different regularizations and numerical methods for the nonlinear Schrödinger equation with singular nonlinearity (sNLSE) including the regularized Lie-Trotter time-spli…
math.NA2022
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation
Weizhu Bao, Yongyong Cai, Feng Yue
Improved uniform error bounds on time-splitting methods are rigorously proven for the long-time dynamics of the weakly nonlinear Dirac equation (NLDE), where the nonlinearity stren…