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## A new double-step method for solving complex Helmholtz equation

#### Tahereh SALİMİ SİAHKOALAEİ [1] , Davod KHOJASTEH SALKUYEH [2]

We present a new double-step iteration method for solving the systems of linear equations that arise from finite difference discretizations of the complex Helmholtz equations. Convergence analysis of the method is discussed. An upper bound on the spectral radius of the iteration matrix of the method is presented and the parameter which minimizes this upper bound is computed. The proposed method is compared theoretically and numerically with some existing methods.

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Complex Helmholtz equation, iterative method, complex linear systems, symmetric positive definite, double-step method
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Primary Language en Mathematics Mathematics Orcid: 0000-0003-2121-2005Author: Tahereh SALİMİ SİAHKOALAEİ Institution: University of GuilanCountry: Iran Orcid: 0000-0003-0228-8565Author: Davod KHOJASTEH SALKUYEH (Primary Author)Institution: University of GuilanCountry: Iran Publication Date : August 6, 2020
 Bibtex @research article { hujms494876, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1245 - 1260}, doi = {10.15672/hujms.494876}, title = {A new double-step method for solving complex Helmholtz equation}, key = {cite}, author = {Sali̇mi̇ Si̇ahkoalaei̇, Tahereh and Khojasteh Salkuyeh, Davod} } APA Sali̇mi̇ Si̇ahkoalaei̇, T , Khojasteh Salkuyeh, D . (2020). A new double-step method for solving complex Helmholtz equation . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1245-1260 . DOI: 10.15672/hujms.494876 MLA Sali̇mi̇ Si̇ahkoalaei̇, T , Khojasteh Salkuyeh, D . "A new double-step method for solving complex Helmholtz equation" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1245-1260 Chicago Sali̇mi̇ Si̇ahkoalaei̇, T , Khojasteh Salkuyeh, D . "A new double-step method for solving complex Helmholtz equation". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1245-1260 RIS TY - JOUR T1 - A new double-step method for solving complex Helmholtz equation AU - Tahereh Sali̇mi̇ Si̇ahkoalaei̇ , Davod Khojasteh Salkuyeh Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.494876 DO - 10.15672/hujms.494876 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1245 EP - 1260 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.494876 UR - https://doi.org/10.15672/hujms.494876 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A new double-step method for solving complex Helmholtz equation %A Tahereh Sali̇mi̇ Si̇ahkoalaei̇ , Davod Khojasteh Salkuyeh %T A new double-step method for solving complex Helmholtz equation %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.494876 %U 10.15672/hujms.494876 ISNAD Sali̇mi̇ Si̇ahkoalaei̇, Tahereh , Khojasteh Salkuyeh, Davod . "A new double-step method for solving complex Helmholtz equation". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1245-1260 . https://doi.org/10.15672/hujms.494876 AMA Sali̇mi̇ Si̇ahkoalaei̇ T , Khojasteh Salkuyeh D . A new double-step method for solving complex Helmholtz equation. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1245-1260. Vancouver Sali̇mi̇ Si̇ahkoalaei̇ T , Khojasteh Salkuyeh D . A new double-step method for solving complex Helmholtz equation. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1245-1260.

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