Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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TL;DR: In this article, the convergence of product integration rules, based on cubic spline interpolation at equally spaced nodes, with "not-a-knot" end condition, is investigated for integrand functions with a interior or endpoint singularity in the integration interval.
Abstract: In this paper the convergence of product integration rules, based on cubic spline interpolation at equally spaced nodes, with "not-a-knot" end condition, is investigated for integrand functions with a interior or endpoint singularity in the integration interval.
10 citations
TL;DR: In this article, a numerical method is proposed for the numerical solution of a linear system with suitable initial and boundary conditions using the cubic B-spline collocation scheme to determine th...
Abstract: In this paper, a numerical method is proposed for the numerical solution of a linear system with suitable initial and boundary conditions using the cubic B-spline collocation scheme to determine th...
10 citations
TL;DR: In this paper, the authors developed a numerical method based on cubic polynomial spline approximations to solve a generalized Black-Scholes equation and showed that the matrix associated with the discrete operator is an M-matrix, which ensures that the scheme is maximum norm stable.
Abstract: We develop a numerical method based on cubic polynomial spline approximations to solve a a generalized Black-Scholes equation We apply the implicit Euler method for the time discretization and a cubic polynomial spline method for the spatial discretization We show that the matrix associated with the discrete operator is an M-matrix, which ensures that the scheme is maximum-norm stable It is proved that the scheme is second-order convergent with respect to the spatial variable Numerical examples demonstrate the stability, convergence, and robustness of the scheme
10 citations
TL;DR: In this article, necessary and sufficient conditions under which a quadratic spline preserves the positivity of a set of function values in the Hermite interpolation were derived, and it was shown that positive interpolation is always possible over nonnegative function values with suitable parameters.
Abstract: Necessary and sufficient conditions are derived under which a quadratic spline preserves the positivity of a set of function values in the Hermite interpolation. As a corollary it is seen that positive interpolation is always possible over a set of nonnegative function values when a quadratic spline with suitable parameters is used.
10 citations