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一类二次保形拟插值函数的研究 总被引:1,自引:0,他引:1
通过讨论一种保形拟插值的基函数与二次规范B-样条函数之间的关系,提出了一类二次保形拟插值样条函数,得到了这类保形拟插值函数在具有线性再生性质,并保持原有数据点列的单调性和凸性时分别应满足的条件,并给出几个应用实例. 相似文献
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基于分数阶微积分基本定理和三次B样条理论,构造了求解线性Caputo-Fabrizio型分数阶微分方程数值解的三次B样条方法,利用分数阶微积分基本定理将初值问题转化为关于解函数的表达式,再使用三次B样条函数逼近表达式中积分项的被积函数,进而计算了一类Caputo-Fabrizio型分数阶微分方程的数值解.给出了所构造的三次B样条方法的误差估计、收敛性和稳定性的理论证明.数值实验表明,该文数值方法在求解一类Caputo-Fabrizio型分数阶微分方程数值解时具有一定的可行性和有效性,且计算精度和计算效率优于现有的两种数值方法. 相似文献
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基于样条插值的模糊控制算法 总被引:1,自引:0,他引:1
利用三次样条插值函数,直接由控制输入输出数据对建立了控制输入与控制输出之间的映射关系,得到了一元三次样条插值控制算法和二元双三次样条插值控制算法,并将二者分别用于单输入单输出系统和双输入单输出系统的仿真控制.仿真结果表明,上述方法是可行的,并且基于三次样条函数的模糊插值控制,具有响应快,无超调,稳态误差极小等很好的控制效果.其设计简单,不需要过多规则,对稀疏规则库条件下的控制器设计尤为适用. 相似文献
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从三次样条插值的定义出发,通过研究第一类积分方程中未知函数的三次样条函数逼近,给出了第一类积分方程的三次样条插值离散化.利用该离散化形式,将第一类积分方程转化成线性方程组的形式.由于第一类积分方程的求解通常是不适定的,进而引起线性方程组的病态性.最后,为克服线性方程组的病态性,通过引入未知函数的多重光滑化约束,得到第一... 相似文献
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Mehdi Dehghan Mehrdad Lakestani 《Numerical Methods for Partial Differential Equations》2007,23(6):1277-1289
Problems for parabolic partial differential equations with nonlocal boundary conditions have been studied in many articles, but boundary value problems for hyperbolic partial differential equations have so far remained nearly uninvestigated. In this article a numerical technique is presented for the solution of a nonclassical problem for the one‐dimensional wave equation. This method uses the cubic B‐spline scaling functions. Some numerical results are reported to support our study. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
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We develop a numerical technique for a class of singularly perturbed two-point singular boundary value problems on an uniform mesh using polynomial cubic spline. The scheme derived in this paper is second-order accurate. The resulting linear system of equations has been solved by using a tri-diagonal solver. Numerical results are provided to illustrate the proposed method and to compared with the methods in [R.K. Mohanty, Urvashi Arora, A family of non-uniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives, Appl. Math. Comput., 172 (2006) 531–544; M.K. Kadalbajoo, V.K. Aggarwal, Fitted mesh B-spline method for solving a class of singular singularly perturbed boundary value problems, Int. J. Comput. Math. 82 (2005) 67–76]. 相似文献
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Mohan K. Kadalbajoo Kailash C. Patidar 《Journal of Computational Analysis and Applications》2003,5(4):425-451
A numerical method based on cubic spline with adaptive grid is given for the self-adjoint singularly perturbed two point boundary value problems. The scheme derived in this method is second order accurate. Numerical examples are given to support the predicted theory. 相似文献
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The singular perturbation mathematical model plays an important role in modelling fluid processes which arise in applied mechanics. We have either, the stiff system of initial value problems or convection-diffusion problems. When conventional numerical methods are used to obtain the solution, the stepsize must be limited to small values. Any attempt to use a larger step-size results in the production of nonphysical oscillations in the solution.In this paper we have constructed an adaptive spline function to solve initial and boundary value problems of ordinary and partial differential equations. The numerical methods based on the spline relations when applied to the test models produce oscillation free solutions. The numerical results are presented and discussed. 相似文献
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In this paper we have presented a method based on cubic splines for solving a class of singular two-point boundary value problems. The original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by Thomas algorithm. Some model problems are solved, and the numerical results are compared with exact solution. 相似文献
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Guan-Rong Chen 《计算数学(英文版)》1992,10(4):339-347
Optimal interpolation problems of scattered data on a circular domain with two different types of boundary value conditions are studied in this paper. Closed-form optimal solutions, a new type of spline functions defined by partial differential operators, are obtained. This type of new splines is a generalization of the well-known $L_g$-splines and thin-plate splines. The standard reproducing kernel structure of the optimal solutions is demonstrated. The new idea and technique developed in this paper are finally generalized to solve the same interpolation problems involving a more general class of partial differential operators on a general region. 相似文献
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构造了一种C^1连续的保单调的有理三次插值函数。由于函数表达式中含有调节参数,使得插值曲线更具灵活性。 相似文献
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A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The authors show that the approximate solutions obtained by the numerical algorithm developed by using nonpolynomial quintic spline functions are better than those produced by other spline and domain decomposition methods. The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach. 相似文献