A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ 2 + h 4 ). It is shown by...A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ 2 + h 4 ). It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ 3 + h 6 ) is gained with once Richardson's extrapolation. Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.展开更多
We consider the(2+1)-dimensional nonlinear Schrodinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank-Nicolson alternating direction implicit difference scheme,which c...We consider the(2+1)-dimensional nonlinear Schrodinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank-Nicolson alternating direction implicit difference scheme,which can also be used to solve general boundary problems under the premise of ensuring accuracy.We use linear Fourier analysis to verify the unconditional stability of the scheme.To demonstrate the effectiveness of the scheme,we compare the numerical results with the exact soliton solutions.Moreover,by using the scheme,we test the stability of the solitons under the small environmental disturbances.展开更多
文摘A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ 2 + h 4 ). It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ 3 + h 6 ) is gained with once Richardson's extrapolation. Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.
文摘We consider the(2+1)-dimensional nonlinear Schrodinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank-Nicolson alternating direction implicit difference scheme,which can also be used to solve general boundary problems under the premise of ensuring accuracy.We use linear Fourier analysis to verify the unconditional stability of the scheme.To demonstrate the effectiveness of the scheme,we compare the numerical results with the exact soliton solutions.Moreover,by using the scheme,we test the stability of the solitons under the small environmental disturbances.
