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Fourth-order compact schemes of a heat conduction problem with Neumann boundary conditions. (English) Zbl 1132.65083
Author’s abstract: The authors present a fourth-order accurate compact finite difference scheme for solving a one-dimensional heat conduction problem with Neumann boundary conditions. The scheme is obtained by applying the compact finite difference to all interior points and the combined compact finite difference to the boundary points. It is shown that the scheme is globally solvable and unconditionally stable. Numerical examples are provided to verify the accuracy.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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