TY - JOUR
T1 - A higher-order compact LOD method and its extrapolations for nonhomogeneous parabolic differential equations
AU - Wang, Tao
AU - Wang, Yuan Ming
PY - 2014/6/15
Y1 - 2014/6/15
N2 - A higher-order compact locally one-dimensional (LOD) finite difference method for two-dimensional nonhomogeneous parabolic differential equations is proposed. The resulting scheme consists of two one-dimensional tridiagonal systems, and all computations are implemented completely in one spatial direction as for one-dimensional problems. The solvability and the stability of the scheme are proved almost unconditionally. The error estimates are obtained in the discrete H1,L2 and ∞ norms, and show that the proposed compact LOD method has the accuracy of the second-order in time and the fourth-order in space. Two Richardson extrapolation algorithms are presented to increase the accuracy to the fourth-order and the sixth-order in both time and space when the time step is proportional to the spatial mesh size. Numerical results demonstrate the accuracy of the compact LOD method and the high efficiency of its extrapolation algorithms.
AB - A higher-order compact locally one-dimensional (LOD) finite difference method for two-dimensional nonhomogeneous parabolic differential equations is proposed. The resulting scheme consists of two one-dimensional tridiagonal systems, and all computations are implemented completely in one spatial direction as for one-dimensional problems. The solvability and the stability of the scheme are proved almost unconditionally. The error estimates are obtained in the discrete H1,L2 and ∞ norms, and show that the proposed compact LOD method has the accuracy of the second-order in time and the fourth-order in space. Two Richardson extrapolation algorithms are presented to increase the accuracy to the fourth-order and the sixth-order in both time and space when the time step is proportional to the spatial mesh size. Numerical results demonstrate the accuracy of the compact LOD method and the high efficiency of its extrapolation algorithms.
KW - Compact locally one-dimensional method
KW - Error estimate
KW - Finite difference method
KW - Parabolic differential equation
KW - Richardson extrapolation
UR - https://www.scopus.com/pages/publications/84899081812
U2 - 10.1016/j.amc.2014.03.139
DO - 10.1016/j.amc.2014.03.139
M3 - 文章
AN - SCOPUS:84899081812
SN - 0096-3003
VL - 237
SP - 512
EP - 530
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -