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A high‐order compact boundary value method for solving one‐dimensional heat equations
Author(s) -
Sun Haiwei,
Zhang Jun
Publication year - 2003
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10076
Subject(s) - discretization , mathematics , variable (mathematics) , boundary value problem , partial differential equation , stability (learning theory) , scheme (mathematics) , compact finite difference , crank–nicolson method , order (exchange) , finite difference method , mathematical analysis , class (philosophy) , finite difference , partial derivative , boundary (topology) , computer science , finance , machine learning , artificial intelligence , economics
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. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 846–857, 2003.