共查询到19条相似文献,搜索用时 156 毫秒
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将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效. 相似文献
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The Cubic B-Spline Method for a Class of Caputo-Fabrizio Fractional Differential Equations北大核心CSCD
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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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基于紧支撑样条小波函数插值与定积分的思想,给出了由紧支撑样条小波插值函数构造数值积分公式的方法.并将该方法应用于二次、三次、四次和五次紧支撑样条小波函数,得到了相应的数值积分公式.最后,通过数值例子验证,发现该方法得到的数值积分公式是准确的,且具有较高精度. 相似文献
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本文构造了一种三次三角样条函数 ,函数的每一段由三个函数值生成 ,具有C3连续性和较好的逼近性 ,可方便地进行插值 .基于同样的方法得出了一种C3连续的三角样条曲线 ,曲线也有较好的逼近性 ,而且具有局部性、保凸性等特性 . 相似文献
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本文在Ⅱ型剖分下,研究一类二元二次分片多项式插值样条函数,采用局部坐标系和本文定理1的拼接技巧,揭示了二元二次样条与一元二次样条之间的紧密联系.只要在垂直网线和水平网线上先构造出一元二次样条并求出它们在节点上的一些数据,就可直接写出二元二次样条的分块解析表示式.利用这种技巧,可以进一步研究各种类型的插值样条,还可用来研究双周期或单周期的插值样条.本文证明了,这类样条函数具有与一元二次样条相同的逼近阶,具体来讲,在不均匀剖分且 f(x,y)∈σ~3[a,b;c,d]时,它的逼近阶是2,在均匀剖分且 f(x,y)∈σ~4[a,b;c,d]时,其逼近阶是3.用本文的方法去研究其他各类插值样条,发现也有这种逼近性质. 相似文献
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加权有理三次插值的逼近性质及其应用 总被引:7,自引:0,他引:7
利用带导数和不带导数的分母为线性的有理三次插值样条构造了一类加权有理三次插值函数,利用这种插值方法,将样条曲线严格约束于给定的折线之上、之下或之间的问题都可以得到解决同时还研究了这种加权有理三次插值的逼近性质。 相似文献
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In the present work we derive higher order variational integrators and combine them with phase lag properties for the numerical integration of systems with oscillatory solutions. The discrete Lagrangian in any time interval is defined as a weighted sum of the evaluation of the continuous Lagrangian at intermediate time nodes. The expressions used for configurations and velocities use linear interpolation, cubic spline interpolation or interpolation via trigonometric functions. The new methods depend on a frequency, which needs to be chosen appropriately. Results show that the energy error of the integration method is decreased for good frequency estimates. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Alexandru Mihai Bica 《Numerical Algorithms》2011,58(3):351-377
A new numerical method for Fredholm functional integral equations is proposed. The method combines the fixed point technique
with numerical integration and cubic spline interpolation. The convergence and the numerical stability of the method are proved
and tested on some numerical examples. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2008,13(1):174-182
A historical overview of Eulerian codes for the numerical solution of the Vlasov equation is presented, with special attention to characteristic methods. An evaluation of the performance of the cubic spline used for interpolation in the characteristic methods, with respect to other methods of interpolation, will be presented by comparing the solutions obtained by solving numerically different Vlasov–Poisson and Vlasov–Maxwell systems on a fixed Eulerian grid. Some recent developments of characteristic methods in two dimensions will be presented. 相似文献
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Reza Mohammadi 《Numerical Methods for Partial Differential Equations》2013,29(4):1173-1191
The cubic B‐spline collocation scheme is implemented to find numerical solution of the generalized Burger's–Huxley equation. The scheme is based on the finite‐difference formulation for time integration and cubic B‐spline functions for space integration. Convergence of the scheme is discussed through standard convergence analysis. The proposed scheme is of second‐order convergent. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are compared with other results given in literature. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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S. I. Fadeev V. V. Kogai T. M. Khlebodarova V. A. Likhoshvai 《Journal of Applied and Industrial Mathematics》2016,10(1):86-96
Some results are presented of the numerical study of periodic solutions of a nonlinear equation with a delayed argument in connection with themathematical models having real biological prototypes. The problem is formulated as a boundary value problem for a delay equation with the conditions of periodicity and transversality. A spline-collocation finite-difference scheme of the boundary value problem using a Hermitian interpolation cubic spline of the class C 1 with fourth order error is proposed. For the numerical study of the system of nonlinear equations of the finitedifference scheme, the parameter continuation method is used, which allows us to identify possible nonuniqueness of the solution of the boundary value problem and, hence, the nonuniqueness of periodic solutions regardless of their stability. By examples it is shown that the periodic oscillations occur for the parameter values specific to the real molecular-genetic systems of higher species, for which the principle of delay is quite easy to implement. 相似文献
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A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results. 相似文献
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本文研究了一类具有非线性边界条件的反应一扩散一对流方程组的周期解的数值解法,利用上下解作为初始迭代,把求方程组的Jacobi方法和Gauss—Seidel方法和上下解方法结合起来,得到了迭代序列的单调收敛性和方法的收敛性,对方法的稳定性也作了论述。 相似文献
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This paper aims to develop a novel numerical approach on the basis of B-spline collocation method to approximate the solution of one-dimensional and two-dimensional nonlinear stochastic quadratic integral equations. The proposed approach is based on the hybrid of collocation method, cubic B-spline, and bi-cubic B-spline interpolation and Itô approximation. Using this method, the problem solving turns into a nonlinear system solution of equations that is solved by a suitable numerical method. Also, the convergence analysis of this numerical approach has been discussed. In the end, examples are given to test the accuracy and the implementation of the method. The results are compared with the results obtained by other methods to verify that this method is accurate and efficient. 相似文献
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The aim of this paper is to present a new numerical method, which ables one to filter and compute numerical derivatives of a function whose values are known in some points from experimental measurements, inducing noisy data. We use a piecewise cubic spline interpolation to generate a function whose Fourier coefficients give an approximation of the numerical derivatives we are looking for. Error and stability analysis of this numerical algorithm are provided. Numerical results are presented for data smoothing and for the first and second derivatives computed from noisy data. They show that this method gives good numerical results. Comparison with other methods is done. 相似文献