Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise
Abstract
1. Introduction
2. The Additive Noise Case
3. The Multiplicative Noise Case
4. Numerical Simulations
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
References
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EOC | |||||
---|---|---|---|---|---|
0.2 | 1.03 | ||||
1.0310 | 1.0250 | 1.0305 | |||
0.4 | 1.04 | ||||
1.0473 | 1.0370 | 1.0392 | |||
0.6 | 1.05 | ||||
1.0589 | 1.0502 | 1.0516 | |||
0.8 | 1.04 | ||||
1.0335 | 1.0386 | 1.0476 | |||
1 | 1.00 | ||||
0.9874 | 1.0021 | 1.0184 |
EOC | |||||
---|---|---|---|---|---|
0.2 | 1.01 | ||||
1.0247 | 0.99904 | 1.0134 | |||
0.4 | 1.01 | ||||
1.0183 | 1.0082 | 1.0114 | |||
0.6 | 1.02 | ||||
1.0185 | 1.0273 | 1.0281 | |||
0.8 | 1.02 | ||||
1.0032 | 1.0264 | 1.0452 | |||
1 | 1.01 | ||||
1.0057 | 1.0116 | 1.0232 |
EOC | |||||
---|---|---|---|---|---|
0.2 | 1.01 | ||||
1.0046 | 1.0128 | 1.0249 | |||
0.4 | 1.04 | ||||
1.0326 | 1.0336 | 1.0400 | |||
0.6 | 1.07 | ||||
1.0740 | 1.0708 | 1.0725 | |||
0.8 | 1.09 | ||||
1.0864 | 1.0888 | 1.0952 | |||
1 | 1.02 | ||||
1.0123 | 1.0148 | 1.0248 |
EOC | |||||
---|---|---|---|---|---|
0.2 | 1.03 | ||||
1.0224 | 1.0234 | 1.0312 | |||
0.4 | 1.05 | ||||
1.0510 | 1.0471 | 1.0496 | |||
0.6 | 1.08 | ||||
1.0876 | 1.0832 | 1.0831 | |||
0.8 | 1.09 | ||||
1.0908 | 1.0937 | 1.1003 | |||
1 | 1.02 | ||||
1.0117 | 1.0146 | 1.0247 |
EOC | |||||
---|---|---|---|---|---|
0.2 | 1.04 | ||||
1.0583 | 1.0315 | 1.0323 | |||
0.4 | 1.00 | ||||
0.9676 | 1.0045 | 1.0220 | |||
0.6 | 1.04 | ||||
1.0056 | 1.0427 | 1.0638 | |||
0.8 | 1.03 | ||||
1.0480 | 1.0015 | 1.0299 | |||
1 | 1.01 | ||||
1.0011 | 1.0094 | 1.0221 |
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Hoult, J.; Yan, Y. Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise. Mathematics 2024, 12, 365. https://doi.org/10.3390/math12030365
Hoult J, Yan Y. Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise. Mathematics. 2024; 12(3):365. https://doi.org/10.3390/math12030365
Chicago/Turabian StyleHoult, James, and Yubin Yan. 2024. "Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise" Mathematics 12, no. 3: 365. https://doi.org/10.3390/math12030365
APA StyleHoult, J., & Yan, Y. (2024). Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise. Mathematics, 12(3), 365. https://doi.org/10.3390/math12030365