共查询到20条相似文献,搜索用时 13 毫秒
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《Journal of Computational and Applied Mathematics》2006,188(2):265-282
An adaptive collocation method based upon radial basis functions is presented for the solution of singularly perturbed two-point boundary value problems. Using a multiquadric integral formulation, the second derivative of the solution is approximated by multiquadric radial basis functions. This approach is combined with a coordinate stretching technique. The required variable transformation is accomplished by a conformal mapping, an iterated sine-transformation. A new error indicator function accurately captures the regions of the interval with insufficient resolution. This indicator is used to adaptively add data centres and collocation points. The method resolves extremely thin layers accurately with fairly few basis functions. The proposed adaptive scheme is very robust, and reaches high accuracy even when parameters in our coordinate stretching technique are not chosen optimally. The effectiveness of our new method is demonstrated on two examples with boundary layers, and one example featuring an interior layer. It is shown in detail how the adaptive method refines the resolution. 相似文献
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研究利用延拓思想求解边值问题的配置算法,并证明了线性配置解本身具有高精度的逐点强超收敛性. 相似文献
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Collocation with piecewise polynomial functions is developed as a method for solving two-point boundary value problems. Convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems. Some computational examples are presented to illustrate the wide applicability and efficiency of the procedure. 相似文献
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《Journal of Computational and Applied Mathematics》2006,196(1):229-240
Sinc collocation method is proven to provide an exponential convergence rate in solving linear differential equations, even in the presence of singularities. But in order to treat the derivatives on boundaries, people often relied on the finite difference method, which would be expected to limit the accuracy. The present paper develops a Sinc collocation method with boundary treatment for two-point boundary value problems. Numerical results show that the method can directly and efficiently handle the boundary derivatives. 相似文献
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Twin solutions to singular boundary value problems 总被引:5,自引:0,他引:5
Ravi P. Agarwal Donal O'Regan 《Proceedings of the American Mathematical Society》2000,128(7):2085-2094
In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .
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V. A. Nikishkin 《Differential Equations》2011,47(3):446-450
We consider boundary value problems for elliptic operators with constant coefficients in a layer, i.e., in a domain between
two parallel planes. We assume that the Lopatinskii condition and the condition of the unique solvability of an auxiliary
problem for an ordinary differential operator are satisfied. We prove theorems on the solvability and smoothness of solutions
in Sobolev spaces with weight of exponential type. 相似文献
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Summary. We present symmetric collocation methods for linear differential-algebraic boundary value problems without restrictions on
the index or the structure of the differential-algebraic equation. In particular, we do not require a separation into differential
and algebraic solution components. Instead, we use the splitting into differential and algebraic equations (which arises naturally
by index reduction techniques) and apply Gau?-type (for the differential part) and Lobatto-type (for the algebraic part) collocation
schemes to obtain a symmetric method which guarantees consistent approximations at the mesh points. Under standard assumptions,
we show solvability and stability of the discrete problem and determine its order of convergence. Moreover, we show superconvergence
when using the combination of Gau? and Lobatto schemes and discuss the application of interpolation to reduce the number of
function evaluations. Finally, we present some numerical comparisons to show the reliability and efficiency of the new methods.
Received September 22, 2000 / Revised version received February 7, 2001 / Published online August 17, 2001 相似文献
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J. RashidiniaM. Ghasemi 《Journal of Computational and Applied Mathematics》2011,235(8):2325-2342
A numerical method based on B-spline is developed to solve the general nonlinear two-point boundary value problems up to order 6. The standard formulation of sextic spline for the solution of boundary value problems leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations of the problem are generated and applied to construct the numerical algorithm. The error analysis and convergence properties of the method are studied via Green’s function approach. O(h6) global error estimates are obtained for numerical solution of these classes of problems. Numerical results are given to illustrate the efficiency of the proposed method. Results of numerical experiments verify the theoretical behavior of the orders of convergence. 相似文献
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Xiao Ping Xu 《数学学报(英文版)》2011,27(6):1023-1070
Classical non-steady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer
theory of fluid dynamics. In this paper, we introduce various schemes with multiple parameter functions to solve these equations
and obtain many families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations
are used to simplify our arguments. The technique of moving frame is applied in the three-dimensional case in order to capture
the rotational properties of the fluid. In particular, we obtain a family of solutions singular on any moving surface, which
may be used to study turbulence. Many other solutions are analytic related to trigonometric and hyperbolic functions, which
reflect various wave characteristics of the fluid. Our solutions may also help engineers to develop more effective algorithms
to find physical numeric solutions to practical models. 相似文献
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Zhong-qing Wang 《Journal of Computational and Applied Mathematics》2011,235(10):3229-3237
In this paper, we propose a Laguerre spectral method for solving Neumann boundary value problems. This approach differs from the classical spectral method in that the homogeneous boundary condition is satisfied exactly. Moreover, a tridiagonal matrix is employed, instead of the full stiffness matrix encountered in the classical variational formulation of such problems. For analyzing the numerical errors, some basic results on Laguerre approximations are established. The convergence is proved. The numerical results demonstrate the efficiency of this approach. 相似文献
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一类无穷多点边值问题正解的存在性 总被引:1,自引:0,他引:1
陈瑞鹏 《纯粹数学与应用数学》2010,26(3):495-500
研究一类二阶非线性常微分方程无穷多点边值问题正解的存在性,利用不动点指数理论得到了方程至少存在一个正解的若干充分条件. 相似文献
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