TY - JOUR
T1 - A High-Order Compact Boundary Value Method for Solving One-Dimensional Heat Equations
AU - Sun, Haiwei
AU - Zhang, Jun
PY - 2003/11
Y1 - 2003/11
N2 - We combine fourth-order boundary value methods (BVMs) for discretizing the temporal variable with fourth-order compact difference scheme for discretizing the spatial variable to solve one-dimensional heat equations. This class of new compact difference schemes achieve fourth-order accuracy in both temporal and spatial variables and are unconditionally stable due to the favorable stability property of BVMs. Numerical results are presented to demonstrate the accuracy and efficiency of the new compact difference scheme, compared to the standard second-order Crank-Nicolson scheme.
AB - We combine fourth-order boundary value methods (BVMs) for discretizing the temporal variable with fourth-order compact difference scheme for discretizing the spatial variable to solve one-dimensional heat equations. This class of new compact difference schemes achieve fourth-order accuracy in both temporal and spatial variables and are unconditionally stable due to the favorable stability property of BVMs. Numerical results are presented to demonstrate the accuracy and efficiency of the new compact difference scheme, compared to the standard second-order Crank-Nicolson scheme.
KW - BVMs
KW - Compact difference scheme
KW - Crank-Nicolson scheme
KW - Heat equation
KW - Unconditional stability
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U2 - 10.1002/num.10076
DO - 10.1002/num.10076
M3 - Article
AN - SCOPUS:0242371968
SN - 0749-159X
VL - 19
SP - 846
EP - 857
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
IS - 6
ER -