Browsing by Author "Mulugeta Alemnew"

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    Numerical Solutions to Second-Order Differential Equations Using Cubic Hermite Spline Interpolation
    (Addis Ababa University, 2024-08-20) Mulugeta Alemnew; Temesgen Alemu
    In this thesis, we introduce cubic Hermite spline as a highly effective interpolation method for approximating curves using discrete data points. While traditional cubic splines provide a strong foundation for curve interpolation, they often fail to accurately capture curve behavior, particularly in situations where tangent information is essential. Cubic Hermite splines overcome this limitation by incorporating tangent data at each point, leading to smoother and more accurate curve approximations. We offer an in-depth examination of cubic Hermite splines, detailing their mathematical formulation, computational methods, and practical implementation strategies. Using tangent information, cubic Hermite splines deliver greater flexibility in modeling complex curve shapes, making them especially valuable in fields such as computer graphics, animation, and engineering design. Additionally, we present comparative analyses highlighting the benefits of cubic Hermite splines over traditional interpolation techniques, demonstrating their effectiveness in maintaining curve characteristics and reducing interpolation errors. Through both theoretical analysis and practical examples, we demonstrate the versatility and efficiency of cubic Hermite splines in various real-world applications. This thesis aims to be a useful resource for researchers, practitioners, and enthusiasts interested in advanced interpolation techniques for curve approximation and modeling.