In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc...In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.展开更多
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
文摘In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.
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.
