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Comparing Numerical Methods for Infiltration Estimation: A Statistical Approach to Accuracy and Efficiency
Abstract
This study evaluates four numerical methods—Euler, Heun, Runge-Kutta 4th order (RK4), and Adams-Bashforth—in terms of their accuracy and computational efficiency for solving the Horton infiltration model, which is crucial for hydrological studies. The methods were applied to simulate soil infiltration and cumulative recharge, with a focus on determining the most suitable method for practical applications in water resource management, agriculture, and soil conservation. An ANOVA (Analysis of Variance) test was conducted to assess the statistical significance of differences in the results obtained from the methods. The test revealed no significant differences between the methods (p-value = 0.9995), indicating that despite differences in computational complexity and accuracy, the methods produced similar results. The Euler method, being the simplest and fastest, provided acceptable results for shorter simulations or less critical applications, while RK4 and Heun, though more computationally expensive, yielded more accurate estimates. Adams-Bashforth offered a reasonable balance between accuracy and efficiency. This study highlights the importance of selecting the appropriate numerical method based on both accuracy and computational cost, particularly for real-time applications and large-scale simulations in hydrology. The findings suggest that simpler methods like Euler can be used for less critical tasks, while more accurate methods like RK4 should be employed for high-precision modeling in complex hydrological scenarios.
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DOI: http://dx.doi.org/10.55981/risetgeotam.2025.1394
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