Abstract
High-order finite difference methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids. The standard pointwise representation has a second-order accurate local truncation error. We also study two schemes which have a fourth-order accurate local truncation error. One of the high-order schemes is based on generalizations of the Padé approximation. The second scheme is based on high-order approximation to the derivative calculated from the Helmholtz equation itself. A symmetric high-order representation is developed for a Neumann boundary condition. Numerical results are presented on model problems approximated with the developed schemes.
| Original language | English |
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| Pages (from-to) | 343-358 |
| Number of pages | 16 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 163 |
| Issue number | 1-4 |
| DOIs | |
| State | Published - 21 Sep 1998 |