Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions
This study contains an algorithmic solution of the Sine Gordon equation in three space and time dimensional problems. For discretization, the central difference formula is used for the time variable. In contrast, space variable x, y, and z are discretized using the non-polynominal cubic spline funct...
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| Veröffentlicht in: | Thermal science 2023, Vol.27 (4 Part B), p.3155-3170 |
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| container_issue | 4 Part B |
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| container_title | Thermal science |
| container_volume | 27 |
| creator | Sattar, Rabia Ahmad, Muhammad Pervaiz, Anjum Ahmed, Nauman Akgul, Ali Abdullaev, Sherzod Alshaikh, Noorhan Wannan, Rania Asad, Jihad |
| description | This study contains an algorithmic solution of the Sine Gordon equation in
three space and time dimensional problems. For discretization, the central
difference formula is used for the time variable. In contrast, space
variable x, y, and z are discretized using the non-polynominal cubic spline
functions for each. The proposed scheme brings the accuracy of order O(h2 +
k2 + ?2 + ?2h2 + ?2k2 + ?2?2) by electing suitable parametric values. The
paper also discussed the truncation error of the proposed method and
obtained the stability analysis. Numerical problems are elucidated by this
method and compared to results taken from the literature. |
| doi_str_mv | 10.2298/TSCI2304155S |
| format | Article |
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three space and time dimensional problems. For discretization, the central
difference formula is used for the time variable. In contrast, space
variable x, y, and z are discretized using the non-polynominal cubic spline
functions for each. The proposed scheme brings the accuracy of order O(h2 +
k2 + ?2 + ?2h2 + ?2k2 + ?2?2) by electing suitable parametric values. The
paper also discussed the truncation error of the proposed method and
obtained the stability analysis. Numerical problems are elucidated by this
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three space and time dimensional problems. For discretization, the central
difference formula is used for the time variable. In contrast, space
variable x, y, and z are discretized using the non-polynominal cubic spline
functions for each. The proposed scheme brings the accuracy of order O(h2 +
k2 + ?2 + ?2h2 + ?2k2 + ?2?2) by electing suitable parametric values. The
paper also discussed the truncation error of the proposed method and
obtained the stability analysis. Numerical problems are elucidated by this
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three space and time dimensional problems. For discretization, the central
difference formula is used for the time variable. In contrast, space
variable x, y, and z are discretized using the non-polynominal cubic spline
functions for each. The proposed scheme brings the accuracy of order O(h2 +
k2 + ?2 + ?2h2 + ?2k2 + ?2?2) by electing suitable parametric values. The
paper also discussed the truncation error of the proposed method and
obtained the stability analysis. Numerical problems are elucidated by this
method and compared to results taken from the literature.</abstract><doi>10.2298/TSCI2304155S</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| title | Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions |
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