Research Article
Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application
Table 2
Comparison of the exact solutions and numerical solutions for different step lengths at
.
| | Exact solution for (i)-gH differentiable case | Exact solution for (ii)-gH differentiable case | Numerical solution for by RKF method | Numerical solution for by RKF method | Numerical solution for by RKF method | | | | | | | | | | |
| 0 | 0.9960 | 2.9882 | 2.5872 | 3.3928 | 1.1039 | 3.3117 | 1.0100 | 3.0301 | 1.0010 | 3.0030 | 0.1 | 1.0957 | 2.8886 | 2.6075 | 3.3326 | 1.2143 | 3.2013 | 1.1110 | 2.9291 | 1.1011 | 2.9029 | 0.2 | 1.1953 | 2.7890 | 2.6279 | 3.2723 | 1.3247 | 3.0909 | 1.2120 | 2.8281 | 1.2012 | 2.8028 | 0.3 | 1.2949 | 2.6894 | 2.6482 | 3.2121 | 1.4351 | 2.9805 | 1.3130 | 2.7271 | 1.3013 | 2.7027 | 0.4 | 1.3945 | 2.5897 | 2.6685 | 3.1519 | 1.5455 | 2.8701 | 1.4141 | 2.6261 | 1.4014 | 2.6026 | 0.5 | 1.4941 | 2.4901 | 2.6888 | 3.0916 | 1.6558 | 2.7597 | 1.5151 | 2.5251 | 1.5015 | 2.5025 | 0.6 | 1.5937 | 2.3905 | 2.7091 | 3.0314 | 1.7662 | 2.6493 | 1.6161 | 2.4241 | 1.6016 | 2.4024 | 0.7 | 1.6933 | 2.2909 | 2.7295 | 2.9711 | 1.8766 | 2.5390 | 1.7171 | 2.3231 | 1.7017 | 2.3023 | 0.8 | 1.7929 | 2.1913 | 2.7498 | 2.9109 | 1.9870 | 2.4286 | 1.8181 | 2.2221 | 1.8018 | 2.2022 | 0.9 | 1.8925 | 2.0917 | 2.7701 | 2.8507 | 2.0974 | 2.3182 | 1.9191 | 2.1211 | 1.9019 | 2.1021 | 1 | 1.9921 | 1.9921 | 2.7904 | 2.7904 | 2.2078 | 2.2078 | 2.0201 | 2.0201 | 2.0020 | 2.0020 |
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