New Conservative Schemes for Zakharov Equation

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2023

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Association of Mathematicians (MATDER)

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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New first-order and second-order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also massconserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We have obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also demonstrate that the new energy-preserving schemes accurately simulate the soliton evolution of the Zakharov system. © MatDer.

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equation. Average vector field method, Hamiltonian system, partitioned average vector field method, Zakharov

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Turkish Journal of Mathematics and Computer Science

Volume

15

Issue

2

Start Page

277

End Page

293

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https://doi.org/10.47000/tjmcs.1226770
 https://search.trdizin.gov.tr/tr/yayin/detay/1218706/new-conservative-schemes-for-zakharov-equation
 https://hdl.handle.net/20.500.14411/7373

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