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991.
Pradip Roul Kiran Thula VMK Prasad Goura 《Mathematical Methods in the Applied Sciences》2019,42(8):2613-2630
This paper is concerned with the numerical solutions of Bratu‐type and Lane‐Emden–type boundary value problems, which describe various physical phenomena in applied science and technology. We present an optimal collocation method based on quartic B‐spine basis functions to solve such problems. This method is constructed by perturbing the original problem and on a uniform mesh. The method has been tested by four nonlinear examples. In order to show the advantage of the new method, numerical results are compared with those obtained by some of the existing methods, such as normal quartic B‐spline collocation method and the finite difference method (FDM). It has been observed that the order of convergence of the proposed method is six, which is two orders of magnitude larger than the normal quartic B‐spline collocation method. Moreover, our method gives highly accurate results than the FDM. 相似文献
992.
Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts. 相似文献
993.
Two deterministic schemes are proposed to realize the assisted clone of an unknown four-particle entangled cluster- type state. The schemes include two stages. The first stage requires teleportation via maximal entanglement as the quantum channel. In the second stages of the protocols, two novel sets of mutually orthogonal basis vectors are constructed, With the assistance of the preparer through a four-particle or two-step two-particle projective measurement under these bases, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, the proposed schemes generate the unknown state deterministically. 相似文献
994.
Renjin Jiang 《Journal of Functional Analysis》2011,261(12):3549-3584
Let (X,d) be a complete, pathwise connected metric measure space with a locally Ahlfors Q-regular measure μ, where Q>1. Suppose that (X,d,μ) supports a (local) (1,2)-Poincaré inequality and a suitable curvature lower bound. For the Poisson equation Δu=f on (X,d,μ), Moser-Trudinger and Sobolev inequalities are established for the gradient of u. The local Hölder continuity with optimal exponent of solutions is obtained. 相似文献
995.
996.
Bijaya Laxmi Panigrahi Gnaneshwar Nelakanti 《Applied mathematics and computation》2011,218(4):1222-1232
We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by the Galerkin method using wavelet bases. By truncating the Galerkin operator, we obtain a sparse representation of a matrix eigenvalue problem. We prove that the error bounds for the eigenvalues and for the distance between the spectral subspaces are of the orders O(nμ-2nr) and O(μ-nr), respectively, where μ−n denotes the norm of the partition and r denotes the order of the wavelet basis functions. By iterating the eigenvectors, we show that the error bounds for the eigenvectors are of the order O(nμ-2nr). We illustrate our results with numerical results. 相似文献
997.
998.
We consider the problem of finding a strictly fundamental cycle basis of minimum weight in the cycle space associated with an undirected connected graph G, where a nonnegative weight is assigned to each edge of G and the total weight of a basis is defined as the sum of the weights of all the cycles in the basis. Several heuristics have been proposed to tackle this NP-hard problem, which has some interesting applications. In this paper we show that this problem is APX-hard, even when restricted to unweighted graphs, and hence does not admit a polynomial-time approximation scheme, unless P=NP. Using a recent result on the approximability of lower-stretch spanning trees (Elkin et al. (2005) [7]), we obtain that the problem is approximable within O(log2nloglogn) for arbitrary graphs. We obtain tighter approximability bounds for dense graphs. In particular, the problem restricted to complete graphs admits a polynomial-time approximation scheme. 相似文献
999.
In this study, we introduce a new design methodology of fuzzy radial basis function-based polynomial neural networks. In many cases, these models do not come with capabilities to deal with granular information. With this regard, fuzzy sets offer several interesting and useful opportunities. This study presents the development of fuzzy radial basis function-based neural networks augmented with virtual input variables. The performance of the proposed category of models is quantified through a series of experiments, in which we use two machine learning data sets and two publicly available software development effort data. 相似文献
1000.
Byeong-Chun Shin 《Applied Numerical Mathematics》2011,61(8):911-928
Differential equations with singular sources or discontinuous coefficients yield non-smooth or even discontinuous solutions. This problem is known as the interface problem. High-order numerical solutions suffer from the Gibbs phenomenon in that the accuracy deteriorates if the discontinuity is not properly treated. In this work, we use the spectral and radial basis function methods and present a least squares collocation method to solve the interface problem for one-dimensional elliptic equations. The domain is decomposed into multiple sub-domains; in each sub-domain, the collocation solution is sought. The solution should satisfy more conditions than the given conditions associated with the differential equations, which makes the problem over-determined. To solve the over-determined system, the least squares method is adopted. For the spectral method, the weighted norm method with different scaling factors and the mixed formulation are used. For the radial basis function method, the weighted shape parameter method is presented. Numerical results show that the least squares collocation method provides an accurate solution with high efficacy and that better accuracy is obtained with the spectral method. 相似文献