In this paper, we developed a collocation method based on Cubic B-spline for solving nonlinear inverse parabolic partial differential equations as the following form ut = [f(u) ux]x + φ (x, t, u, ux), 0 < x < 1, 0  t  T, where f(u) and φ are smooth functions defined on R. First, we obtained a time discrete scheme by approximating the first-order time derivative via forward finite difference formula, then we used Cubic B-spline collocation method to approximate the spatial derivatives and Tikhonov regularization method for solving produced illposed system. It is proved that the proposed method has the order of convergence O(k+h2). The accuracy of the proposed method is demonstrated by applying it on three test problems. Figures and comparisons have been presented for clarity. The aim of this paper is to show that the collocation method based on Cubic B-spline is also suitable for the treatment of the nonlinear inverse parabolic partial differential equations.

In this paper, we apply a numerical scheme for the solution of a second order partial integro-differential equation with a weakly singular kernel. In the time direction, the backward Euler method time-stepping is used to approximate the differential term and the Cubic B-splines is applied to the space discretization. Detailed discrete schemes, the convergence and the stability of the method is demonstrated. Next, the computational efficiency and accuracy of the method are examined by the numerical results.

In this study, we develop a precise and effective numerical approach to solve the time--fractional Black--Scholes equation, which is used to calculate European options. The method employs Cubic B-spline collocation for spatial discretization and a finite difference method for time discretization. An  analysis of the method's stability is conducted. Finally, two numerical examples are included to show the effectiveness and applicability of the suggested method.

In this paper, an algorithm for fast defect detection in cloths based on fast B-spline transform is proposed. The algorithm can be applied to analyzing images at any integer scale for defect information. It can also be extended to a parallel algorithm that decomposes images at all desired scales simultaneously. A threshold parameter δth is used to adjust the defect detection reliability. A desired compromise between fault recognition and continuity of edge pixels can be reached by adjusting the value of δth properly.

Purpose: In this paper, we will consider the interpolation of fuzzy data by using the fuzzy-valued piecewise quartic polynomials Qy0, y1, ..., yn (x) induced from E (3) Cubic spline functions.Method: It has been many years since researchers have attended to the problem of interpolation of fuzzy data. Here, for Lagrange interpolation of fuzzy data, we will use the piecewise quartic polynomial induced from E (3) Cubic spline functions to interpolate the fuzzy data. To do this, we will apply the extension principle to construct the membership function of Qy0, y1, ..., yn (x). Results: By using piecewise quartic polynomials, a new set of fuzzy spline functions was defined to interpolate given fuzzy data.Conclusions: In our previous study, we used E (3) Cubic spline to construct E (3) fuzzy Cubic spline. In this article, we added one extra term to this spline to compute the piecewise quartic polynomials and hence the fuzzy-valued piecewise quartic polynomials.