Ishak Hashim¹, Nur Nabilah Che Draman², Samsul Ariffin Abdul Karim^3,*, Wee Ping Yeo⁴, Dumitru Baleanu^5,6,7

CMC-Computers, Materials & Continua, Vol.69, No.1, pp. 221-236, 2021, DOI:10.32604/cmc.2021.016006

Abstract This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with continuity everywhere. We derive the condition on each adjacent triangle. On each triangular patch, we employ convex combination method between three local schemes. The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets. We tested the proposed scheme with 36,65, and 100 data points for some well-known test functions. The scheme is also applied to interpolate the data for the electric potential. We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin (PS)… More >

Kamil Khan¹, Arshed Ali^1,*, Fazal-i-Haq², Iltaf Hussain³, Nudrat Amir⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 673-692, 2021, DOI:10.32604/cmes.2021.012730

Abstract This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used for interpolation in both methods. The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations. The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values. An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method… More >

Siraj-ul-Islam¹, Arshed Ali^2,*, Aqib Zafar¹, Iltaf Hussain¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 915-935, 2020, DOI:10.32604/cmes.2020.011218

Abstract Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency, and is mentioned as potential alternative of conventional numerical methods. In this paper, a differential quadrature based numerical scheme is developed for solving volterra partial integro-differential equation of second order having a weakly singular kernel. The scheme uses cubic trigonometric B-spline functions to determine the weighting coefficients in the differential quadrature approximation of the second order spatial derivative. The advantage of this approximation is that it reduces the problem to a first order time dependent integro-differential equation (IDE). The proposed scheme is obtained in… More >