Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations
Archna Kumari, V. K. Kukreja
Abstract
With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article.
Topics & Concepts
Hermite interpolationHermite polynomialsGeneralizationCubic Hermite splineHermite splineInterpolation (computer graphics)MathematicsMonotone cubic interpolationApplied mathematicsDifferential equationDifferential (mechanical device)Algebra over a fieldComputer scienceAlgorithmMathematical analysisSpline interpolationPure mathematicsPolynomial interpolationPolynomialNearest-neighbor interpolationLinear interpolationEngineeringArtificial intelligenceStatisticsMotion (physics)Aerospace engineeringBilinear interpolationSmoothing splineFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods for differential equations