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In this paper, an unconditionally stable implicit difference scheme based on quartic spline interpolations in space direction and finite difference discretization in time direction for the numerical solution of two-dimensional linear hyperbolic equation is proposed. The proposed scheme is second-order accurate in time direction and fourth-order accurate in space direction. Numerical examples are tested...
Let Omega be a regular triangulation of a two dimensional domain and Snr(Omega) be a vector space of functions in Cr whose restriction to each small triangle in Omega is a polynomial of total degree at most n. Dimensions of bivariate spline spaces Snr(Omega) over a special kind of triangulation, called the unconstricted triangulation, were given by Farin in the paper [J. Comput. Appl. Math. 192(2006),...
Let Delta be an arbitrary regular triangulation of a simply connected domain and I1Delta be a restrictive appointed point triangulation related to A. In this paper, employing the well-known Bezier-net method, we study the algebraic structure of bivariate C1 quadratic weak spline space W21(I1Delta).
In this paper, by using the coloring method, the Bezier-net method and the technique of minimal determining set, a kind of Lagrange interpolation schemes by bivariate C1 cubic splines with boundary conditions on nonuniform type-2 triangulations is constructed and a locally supported dual basis of bivariate C1 cubic splines space with boundary conditions on nonuniform type-2 triangulations is given.
In this paper, a new difference scheme by using cubic splines for solving a singularly-perturbed two-point boundary-value problem for second-order ordinary differential equations is derived. The proposed scheme is fourth order accurate, which is better than previous published results. Finally, two numerical examples are solved to illustrate the efficiency of our method.
It is well-known that, the algebraic structure of bivariate spline spaces over arbitrary regular triangulations is an extremely complicated problem. Therefore, people turned to study bivariate spline spaces over some special triangulations. In this paper, by using the Bezier-net method and the technique of minimal determining sets,the dimension of bivariate sextic C2 spline space over a kind of generalized...
In this paper, a difference scheme based on the quartic splines for solving the singularly-perturbed two-point boundary-value problem of second-order ordinary differential equations subject to Neumann-type boundary conditions are derived. The accuracy order of the schemes is O(h4) not only at the interior nodal points but also at the two endpoints, which are better than general center finite difference...
In this paper, by using the technique of B-net method and the minimal determining set, the dimension of the space of bivariate C1 cubic spline functions on a kind of refined triangulation, called Wang's refinement, is determined, and a set of dual basis with local support is given.
In this paper, by employing bivariate cubic C-1 B-splines, a bivariate B-spline finite element method is presented to solve bending problems of rectangular plates. In comparison with analytical solutions, it is found that, for various boundary conditions and different loading conditions, the accuracy of the present numerical method is very satisfactory.
In this paper, a numerical method based on non-polynomial spline functions is presented to solve the one-dimensional heat equation. The new method is unconditionally stable. The accuracy order of the new method is of O(k5+h4),where k and h denote the mesh parameters for t and x, respectively. The accuracy of the present method is much higher than previous known methods.
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