NONITERATIVE SOLUTION OF A BOUNDARY VALUE PROBLEM OF THE HELMHOLTZ TYPE.
Physical sciences research papers,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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A noniterative method for solving difference equations of the Helmholtz type in a discretized rectangular domain with uniform grid spacing is presented. This method is an improvement over existing direct methods for the same problem, in terms of both the accuracy and computer storage required. The scheme involves writing a system of linear algebraic equations in the form of a system of matrix equations, applying an orthogonal transformation to this system, reordering the unknowns of the transformed system, and computing the solution of this system by a simple recursion formula. The efficiency, accuracy, and storage demands of this method are compared with existing numerical schemes for solving the same problem. In extreme cases, the computing effort required by the present scheme is only about 30 percent that of the point successive overrelaxation method. For a system having IxI unknowns, the storage demand is at the most about oneI that of other direct methods. Author
- Theoretical Mathematics