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Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

Hadhoud Adel R., Alaal Faisal E. Abd, Abdelaziz Ayman A., Radwan Taha

Demonstratio Mathematica

2021

Vol. 54, nr 1

436--451

In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

An Example of Two-Dimensional Interpolation Using a Linear Combination of Bicubic B-Splines

Rosłoniec S.

International Journal of Electronics and Telecommunications

2011

Vol. 57, No. 3

293-299

The paper describes how a linear combination of bicubic B-splines can be effectively used in a two-dimensional interpolation. It is assumed that values of a function to be interpolated are evaluated at the uniformly located nodes of a corresponding rectangular grid. All formulae of importance have been derived step by step and are presented in a form convenient for computer implementations. To ensure clarity of considerations a short description of one-dimensional B-spline is also given in Appendix 1. The usefulness of the presented interpolation algorithm has been confirmed by the real engineering example of applications.