PRELIMINARY STUDY ON ADAPTIVE KNOT STRATEGIES IN CUBIC B-SPLINES FOR EFFICIENT DIFFERENTIAL EQUATION SOLVING
DOI:
https://doi.org/10.55766/sujst6847Keywords:
Cubic B-splines, Adaptive Node Refinement, Differential Equations, Numerical Methods, Error EstimationAbstract
This preliminary study explores a modest approach that combines cubic B-splines with an adaptive knot refinement algorithm for solving differential equations. The method adjusts knot placement dynamically based on local error estimates, aiming to improve solution accuracy without manual intervention. While the enhancements in accuracy may be limited, particularly in areas with rapid solution changes, the approach provides a foundational framework for further research. Although the improvement in accuracy may seem modest, it lays a solid foundation for further refinement and development, paving the way for even greater advancements in computational precision and efficiency.
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