Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit. (25th June 2021)

• Record Type: Journal Article
• Authors: Khalid, Aasma; Rehan, Akmal; Nisar, Kottakkaran Sooppy; Osman, M S
• Is Part Of: Physica scripta. Volume 96:Number 10(2021)
• Publication Date: 2021-06-25
• Subjects: Non-linear -- Cubic -- absolute error -- B Spline -- linear; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/ac0bd0
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: This study manages the numeric roots of the 7th-order linear & nonlinear boundary value problems(BVPs) utilizing another CB(Cubic-B) spline strategy. Cubic Spline interpolation is a different type of spline interpolation which is utilized very frequently to escape the problem of Runge's phenomenon. That technique provides an interpolating polynomial which is evener and has lesser error than former interpolating polynomials such as Lagrange polynomial and Newton polynomial. The primary thought is that we have altered the BVPs to deliver another framework arrangement of linear equations. We develop the class of numerical techniques for a particular selection of the factors that are associated with CB Spline. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CB Spline is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show the higher level of preciseness of CB Spline, the absolute errors of the CB Spline has been compared with different techniques such as Modified Decomposition Method(MDM), Differential Transform Method(DTM), Homotopy Perturbation Method(HPM), Variational Iteration technique(VIT) and observed to be more accurate. Graphs that describe the graphical comparison of CB Spline at n = 5 and n = 10 are also included in this paper. The calculation created here isn't just for the numeric roots of the 7th-order BVPs. It also evaluates the derivative to the 7th-order derivative of the specific solution. A few models are represented, which depicting the practicality and capability of the suggested conspire.