Nonlinear partial differential equations are widely studied in Applied Mathematics and Physics. The generalized Burgers-Huxley equations play important roles in different nonlinear physics mechanisms. In this paper, we develop a kind of cubic B-spline quasi-interpolation which is used to solve Burgers-Huxley equations. Firstly, the cubic B-spline quasi-interpolation is presented. Next we get the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and modified Euler scheme to approximate the time derivative of the dependent variable. Moreover, the efficiency of the proposed method is illustrated by the agreement between the numerical solution and the analytical solution which indicate the numerical scheme is quite acceptable.
Toric Bézier patches are a multi-sided generalization of classical rational Bézier patches which are widely used in freeform surface modeling. In this article, we study the problem of finding the patch with minimal area among all possible toric Bézier patches with the given boundaries, that is, the Plateau-toric Bézier problem, and obtain an approximation of minimal toric Bézier patch. Some representative examples are given to verify our results.
In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.
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