A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations
Abstract
:1. Introduction
2. Preliminary Concept of the Shehu Transform
3. The Basic Procedure of the T-RPSM
- and for each ,
- If then ,
- .
4. Numerical Applications
4.1. Example 1
4.2. Example 2
5. Description of Results
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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T-RPSM | T-RPSM | T-RPSM | Exact Results | Absolute Error | |
---|---|---|---|---|---|
(0.05, 0.05) | 0.0525636 | 0.504216 | 0.0500677 | 0.0500677 | 00000 |
(0.10, 0.10) | 0.110517 | 0.102396 | 0.1005 | 0.1005 | 00000 |
(0.15, 0.15) | 0.174275 | 0.15664 | 0.151691 | 0.151691 | 00000 |
(0.20, 0.20) | 0.24428 | 0.213726 | 0.204013 | 0.204013 | 00000 |
(0.25, 0.25) | 0.321004 | 0.274168 | 0.257853 | 0.257853 | 00000 |
(0.30, 0.30) | 0.404951 | 0.338458 | 0.313602 | 0.313602 | 00000 |
(0.35, 0.35) | 0.496657 | 0.407079 | 0.371657 | 0.371657 | 00000 |
(0.40, 0.40) | 0.596693 | 0.480515 | 0.432429 | 0.432429 | 00000 |
(0.45, 0.45) | 0.705666 | 0.559263 | 0.496337 | 0.496337 | 00000 |
(0.50, 0.50) | 0.824219 | 0.64383 | 0.563813 | 0.563813 | 00000 |
T-RPSM | T-RPSM | T-RPSM | Exact Results | Absolute Error | |
---|---|---|---|---|---|
(0.05, 0.05) | 0.0389404 | 0.479233 | 0.0496878 | 0.0496878 | 00000 |
(0.10, 0.10) | 0.0606771 | 0.088515 | 0.0975104 | 0.0975104 | 00000 |
(0.15, 0.15) | 0.0711182 | 0.119264 | 0.141641 | 0.141641 | 00000 |
(0.20, 0.20) | 0.075 | 0.139052 | 0.180331 | 0.180331 | 00000 |
(0.25, 0.25) | 0.0768636 | 0.147623 | 0.211944 | 0.211944 | 00000 |
(0.30, 0.30) | 0.0820313 | 0.14535 | 0.234994 | 0.234994 | 00000 |
(0.35, 0.35) | 0.097583 | 0.133078 | 0.248173 | 0.248173 | 00000 |
(0.40, 0.40) | 0.133333 | 0.1121 | 0.250386 | 0.250386 | 00000 |
(0.45, 0.45) | 0.202808 | 0.0836075 | 0.240772 | 0.240772 | 00000 |
(0.50, 0.50) | 0.324219 | 0.0495244 | 0.218726 | 0.218726 | 00000 |
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Liu, J.; Nadeem, M.; Islam, A.; Mureşan, S.; Iambor, L.F. A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations. Symmetry 2023, 15, 2152. https://doi.org/10.3390/sym15122152
Liu J, Nadeem M, Islam A, Mureşan S, Iambor LF. A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations. Symmetry. 2023; 15(12):2152. https://doi.org/10.3390/sym15122152
Chicago/Turabian StyleLiu, Jinxing, Muhammad Nadeem, Asad Islam, Sorin Mureşan, and Loredana Florentina Iambor. 2023. "A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations" Symmetry 15, no. 12: 2152. https://doi.org/10.3390/sym15122152