USING SPLINE FUNCTIONS IN THE APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS
Keywords:
Differential equations, numerical methods, spline functions, interpolation, boundary value problem, matrix, systemAbstract
This article explores the significance and effectiveness of using spline functions in the numerical approximate solution of differential equations. In modern science and engineering, many real-world processes are described by differential equations that often cannot be solved analytically, necessitating the application of numerical methods. The article outlines the mathematical foundations of splines, highlighting their properties of smoothness and high accuracy. It also analyzes methods for converting discrete solutions obtained using spline functions into continuous and smooth functions, as well as their advantages in numerical computations. The article concludes by demonstrating the relevance of spline functions in solving differential equations and their potential for practical application.
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