Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

In this article, we propose a new numerical method based on fractal cubic spline for the numerical approximate solutions of linear and nonlinear singular two-point boundary-value problems. Error analysis of the proposed method is examined and it is shown that proposed method has second-order convergence. Numerical examples are provided to validate the theoretical results. © 2020, Springer Nature India Private Limited.

School of Advanced Sciences

Vellore Campus

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International Journal of Applied and Computational Mathematics

Fractal Cubic Spline Methods for Singular Boundary-Value Problems

In this article, a new α-fractal rational cubic spline is introduced with the help of the iterated function system (IFS) that contains rational functions. The numerator of the rational function contains a cubic polynomial and the denominator of the rational function contains a quadratic polynomial with three shape parameters. The convergence analysis of the α-fractal rational cubic spline is established. By restricting the scaling factors and the shape parameters, the α-fractal rational cubic spline is constrained between two piecewise linear functions whenever interpolation data lies in between two piecewise linear functions. Also, positivity and monotonicity of the α-fractal rational cubic spline are discussed. Numerical examples are provided to support the theoretical results. © 2020, Istituto di Informatica e Telematica (IIT).

Calcolo

Shape preserving α -fractal rational cubic splines

In this article, numerical solutions of nonlinear boundary-value problems are obtained using fractal quintic spline. Convergence analysis of the proposed method is also established. Proposed method has fourth-order convergence. Numerical examples are provided to show practical usefulness of the method and numerical results are compared with the existing numerical methods. © 2020, Hacettepe University. All rights reserved.

Hacettepe Journal of Mathematics and Statistics

Fractal quintic spline method for nonlinear boundary-value problems

A new numerical method is developed for approximating the solution of the fourth-order boundary-value problems with the help fractal quintic spline. The proposed method has second-order convergence. Numerical examples are experimented for the numerical illustration of the proposed method. It is shown that the method developed in this paper is more efficient than the method developed by the quintic spline. © 2019, Springer Nature India Private Limited.

Fractal Quintic Spline Solutions for Fourth-Order Boundary-Value Problems

A new C1-rational cubic fractal interpolation surface is introduced to interpolate the surface data which lies on a rectangular grid. At the beginning, C1-rational cubic fractal interpolation functions are constructed along the grid lines. Then, the C1-rational cubic fractal interpolation surface is constructed with the help of blending functions and the rational cubic fractal interpolation functions. Convergence analysis of the fractal interpolation surface to an original function is carried out. Further, the scaling factors and the shape parameters are constrained, so that the fractal interpolation surface would lie above the fixed plane whenever the surface data lie above the plane. Also, conditions on the scaling factors and the shape parameters are derived to interpolate the convex surface data. © 2018, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Computational and Applied Mathematics

Constrained and convex interpolation through rational cubic fractal interpolation surface

A new type of C1 Fractal Interpolation Function (FIF) is developed using the Iterated Function System (IFS) which contains the rational spline. The numerator of this rational spline contains cubic polynomial and the denominator of the rational spline contains quadratic polynomial. We find uniform error bound between the original function which belongs to the class C2 and the FIF. We described suitable conditions on scaling factors and shape parameters such that they preserve the shape properties which are inherited in the data. © 2017 Elsevier B.V.