Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative
Abstract
:1. Introduction
2. Preliminaries
- 1.
- 2.
- 3.
3. General Procedure of the Proposed Methods
3.1. LRPSM Procedure
- and for each
- .
3.2. NIM Procedure
4. Numerical Problem
5. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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ß | ||||
---|---|---|---|---|
0.1 | 0.49885 | 0.49885 | 5.24347 | 2.65047 |
0.2 | 0.495229 | 0.495229 | 1.03199 | 4.84593 |
0.3 | 0.489206 | 0.489206 | 1.4969 | 6.29355 |
0.4 | 0.480899 | 0.480899 | 1.90139 | 6.74469 |
0.5 | 0.470466 | 0.470466 | 2.23189 | 6.07651 |
0.6 | 0.4581 00 | 0.458100 | 2.47961 | 4.30081 |
0.7 | 0.444021 | 0.444021 | 0.64079 | 1.55325 |
0.8 | 0.428469 | 0.428469 | 2.71647 | 1.93312 |
0.9 | 0.411693 | 0.411693 | 2.71195 | 5.86445 |
1 | 0.39395 | 0.39395 | 2.6359 | 9.92581 |
ß | ||||||
---|---|---|---|---|---|---|
0.1 | 0.434414 | 0.440173 | 0.475125 | 0.476806 | 0.492521 | 0.492951 |
0.2 | 0.442031 | 0.453097 | 0.481234 | 0.484463 | 0.496035 | 0.49686 |
0.3 | 0.448889 | 0.464403 | 0.485383 | 0.489911 | 0.497171 | 0.498328 |
0.4 | 0.455015 | 0.473809 | 0.487534 | 0.493019 | 0.495917 | 0.49732 |
0.5 | 0.460346 | 0.481064 | 0.487657 | 0.493704 | 0.492302 | 0.493848 |
0.6 | 0.46473 | 0.48596 | 0.485733 | 0.49193 | 0.486393 | 0.487977 |
0.7 | 0.467943 | 0.488344 | 0.48176 | 0.487715 | 0.478294 | 0.479817 |
0.8 | 0.469719 | 0.488128 | 0.475755 | 0.481128 | 0.468146 | 0.46952 |
0.9 | 0.469782 | 0.48529 | 0.467762 | 0.472288 | 0.456117 | 0.457274 |
1 | 0.467887 | 0.479877 | 0.457859 | 0.461359 | 0.442404 | 0.443299 |
ß | ||||||
---|---|---|---|---|---|---|
0.1 | −0.189874 | −0.176482 | −0.172736 | −0.169667 | −0.165132 | −0.164485 |
0.2 | −0.17988 | −0.167194 | −0.163645 | −0.160737 | −0.15644 | −0.155828 |
0.3 | −0.169887 | −0.157905 | −0.154553 | −0.151807 | −0.147749 | −0.14717 |
0.4 | −0.159894 | −0.148617 | −0.145462 | −0.142877 | −0.139058 | −0.138513 |
0.5 | −0.1499 | −0.139328 | −0.136371 | −0.133948 | −0.130367 | −0.129856 |
0.6 | −0.139907 | −0.13004 | −0.127279 | −0.125018 | −0.121676 | −0.121199 |
0.7 | −0.129914 | −0.120751 | −0.118188 | −0.116088 | −0.112985 | −0.112542 |
0.8 | −0.11992 | −0.111463 | −0.109096 | −0.107158 | −0.104294 | −0.103885 |
0.9 | −0.109927 | −0.102174 | −0.100005 | −0.0982282 | −0.0956025 | −0.0952279 |
1 | −0.0999335 | −0.0928855 | −0.0909137 | −0.0892983 | −0.0869114 | −0.0865708 |
ß | NIM | LRPSM | Exact | NIM Error | LRPSM Error | HPSTM Error [50] |
---|---|---|---|---|---|---|
0 | 0.991481 | 0.991556 | 0.999998 | 0.00851667 | 0.0084413 | 0.0084617 |
0.2 | 0.972981 | 0.97305 | 0.979642 | 0.00666104 | 0.00659231 | 0.00669431 |
0.4 | 0.915696 | 0.915755 | 0.920231 | 0.00453561 | 0.0044759 | 0.0045769 |
0.6 | 0.821906 | 0.821955 | 0.824134 | 0.00222747 | 0.00217903 | 0.00237503 |
0.8 | 0.695349 | 0.695384 | 0.695181 | 0.00016832 | 0.00020345 | 0.00021345 |
1 | 0.541067 | 0.541087 | 0.538513 | 0.00255363 | 0.00257369 | 0.00267168 |
1.2 | 0.365208 | 0.365212 | 0.360376 | 0.00483206 | 0.0048358 | 0.0039348 |
1.4 | 0.174786 | 0.174773 | 0.167873 | 0.00691323 | 0.0069001 | 0.0069231 |
1.6 | −0.0226073 | -0.022637 | −0.0313235 | 0.00871626 | 0.00868658 | 0.00967657 |
ß | NIM | LRPSM | Exact | NIM Error | LRPSM Error | HPSTM Error [50] |
---|---|---|---|---|---|---|
0 | −0.0000270 | 0.0063208 | 0.002125 | 0.002152 | 0.004195 | 0.006295 |
0.2 | 0.196972 | 0.2032 | 0.200752 | 0.00377968 | 0.00244894 | 0.00256804 |
0.4 | 0.386115 | 0.391976 | 0.391375 | 0.0052597 | 0.00060127 | 0.00070134 |
0.6 | 0.55986 | 0.565119 | 0.566395 | 0.0065352 | 0.00127557 | 0.00138435 |
0.8 | 0.711279 | 0.715728 | 0.718835 | 0.00755558 | 0.00310701 | 0.00321702 |
1 | 0.834339 | 0.837799 | 0.842617 | 0.00827852 | 0.00481835 | 0.00471935 |
1.2 | 0.924135 | 0.926469 | 0.932807 | 0.00867223 | 0.00633839 | 0.00643939 |
1.4 | 0.977091 | 0.978205 | 0.985809 | 0.00871776 | 0.00760327 | 0.00780727 |
1.6 | 0.991098 | 0.990949 | 0.999509 | 0.00841091 | 0.00856015 | 0.00957010 |
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Alzahrani, A.B.M. Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative. Symmetry 2023, 15, 1666. https://doi.org/10.3390/sym15091666
Alzahrani ABM. Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative. Symmetry. 2023; 15(9):1666. https://doi.org/10.3390/sym15091666
Chicago/Turabian StyleAlzahrani, Abdulrahman B. M. 2023. "Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative" Symmetry 15, no. 9: 1666. https://doi.org/10.3390/sym15091666
APA StyleAlzahrani, A. B. M. (2023). Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative. Symmetry, 15(9), 1666. https://doi.org/10.3390/sym15091666