Geodesic
A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods
Applications of Mathematics, Tome 27 (1982) no. 5, pp. 375-390
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The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments performed are studied from the point of view of the time and storage requirements and the achieved accuracy of the solution.
The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments performed are studied from the point of view of the time and storage requirements and the achieved accuracy of the solution.
DOI : 10.21136/AM.1982.103983
Classification : 35J05, 65F05, 65F10, 65N20, 65N22, 86A25
Keywords: comparison; electromagnetic fields in geophysics; numerical experiments; accuracy; Helmholtz equation 
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Červ, Václav; Segeth, Karel. A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods. Applications of Mathematics, Tome 27 (1982) no. 5, pp. 375-390. doi: 10.21136/AM.1982.103983

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