Abstract
Compact methods are high accuracy finite-difference methods where the functions and their derivatives are considered as unknowns. Two methods are presented to eliminate the second-order derivatives in parabolic equations, while keeping the fourth-order accuracy and the tridiagonal nature of the schemes. A type of high accuracy additional boundary condition is also proposed, which is consistent with the high accuracy of the inner scheme and uses only values at interior and boundary nodes. Integration on nonregular meshes is also examined.
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