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Analysis of Compact Symmetric Finite Difference Methods with Highest Possible Orders for Elliptic Equations
For the $d$-dimensional variable-coefficient Poisson problem $-\nabla \cdot(a\nabla u)=f$ subject to Dirichlet boundary conditions, we seek compact (i.e., $3^d$-point) symmetric finite difference methods (FDMs) of the highest possible consistency orders, which yield symmetric positive definite (SPD)
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