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October 23, 2025Open Access

Second Order L1 Schemes for Fractional Differential Equations

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Second order numerical methods improve approximations of fractional derivatives in differential equations, implying enhanced solution accuracy.

Numerical methods achieve second-order accuracy in fractional differential equations and ordinary differential equations, validating theoretical predictions.
The analysis uses parameter-dependent approximations and the zeta function to derive expansion formulas for fractional derivatives.
Comparison with ordinary differential equations illustrates the practical applications and computational viability of these second-order methods.
This approach highlights improvements in accuracy, showcasing the relevance of these techniques in mathematical modeling and simulations.

Dimitrov et al. (2025) studied this question.

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Second order numerical methods improve approximations of fractional derivatives in differential equations, implying enhanced solution accuracy.