2,503 research outputs found
AN ENHANCED WAVELET BASED METHOD FOR NUMERICAL SOLUTION OF HIGH ORDER BOUNDARY VALUE PROBLEMS
The Legendre wavelet collocation method (LWCM) is suggested in this study for solving high-order boundary value problems numerically. Eighth, tenth, and twelfth-order examples are used as test problems to ensure that the technique is efficient and accurate. In comparison to other approaches, the numerical results obtained using LWCM demonstrate that the method's accuracy is very good. The results indicate that the method requires less computational effort to achieve better results
Modified Variational Iteration Method with Chebyshev Polynomials for Solving 12th order Boundary Value problems
We consider in this paper an illustration of the modified variational iteration method (MVIM) as an effective and accurate solver of 12th order boundary value problem (BVP). For this reason, the Chebyshev polynomials of the principal kind was utilized as a premise capabilities in the guess of the logical capability of the given issue. The strategy is applied in an immediate manner without utilizing linearization or irritation. The subsequent mathematical confirmations recommend that the strategy is without a doubt successful and exact as applied to a few direct and nonlinear issues as mathematical trial and error. Maple 18 was used for all computational simulations carried out in this research.©2022 JNSMR UIN Walisongo. All rights reserved
Modified Variational Iteration Method with Chebyshev Polynomials for Solving 12th order Boundary Value problems
We consider in this paper an illustration of the modified variational iteration method (MVIM) as an effective and accurate solver of 12th order boundary value problem (BVP). For this reason, the Chebyshev polynomials of the principal kind was utilized as a premise capabilities in the guess of the logical capability of the given issue. The strategy is applied in an immediate manner without utilizing linearization or irritation. The subsequent mathematical confirmations recommend that the strategy is without a doubt successful and exact as applied to a few direct and nonlinear issues as mathematical trial and error. Maple 18 was used for all computational simulations carried out in this research.©2022 JNSMR UIN Walisongo. All rights reserved
Sampling and Reconstruction of Shapes with Algebraic Boundaries
We present a sampling theory for a class of binary images with finite rate of
innovation (FRI). Every image in our model is the restriction of
\mathds{1}_{\{p\leq0\}} to the image plane, where \mathds{1} denotes the
indicator function and is some real bivariate polynomial. This particularly
means that the boundaries in the image form a subset of an algebraic curve with
the implicit polynomial . We show that the image parameters --i.e., the
polynomial coefficients-- satisfy a set of linear annihilation equations with
the coefficients being the image moments. The inherent sensitivity of the
moments to noise makes the reconstruction process numerically unstable and
narrows the choice of the sampling kernels to polynomial reproducing kernels.
As a remedy to these problems, we replace conventional moments with more stable
\emph{generalized moments} that are adjusted to the given sampling kernel. The
benefits are threefold: (1) it relaxes the requirements on the sampling
kernels, (2) produces annihilation equations that are robust at numerical
precision, and (3) extends the results to images with unbounded boundaries. We
further reduce the sensitivity of the reconstruction process to noise by taking
into account the sign of the polynomial at certain points, and sequentially
enforcing measurement consistency. We consider various numerical experiments to
demonstrate the performance of our algorithm in reconstructing binary images,
including low to moderate noise levels and a range of realistic sampling
kernels.Comment: 12 pages, 14 figure
A Reproducing Kernel Perspective of Smoothing Spline Estimators
Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.equivalent kernels, nonparametric regression, Hilbert spaces, time series filtering, spectral properties
Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft, supplemental data
Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables
On Higher Order Boundary Value Problems Via Power Series Approximation Method
In this work, a relatively new technique called Power Series Approximation Method (PSAM) is applied for the numerical approximate solution of non-linear higher order boundary value problems. Several examples are given to illustrate the efficiency and implementation of the method. The proposed method is efficient and effective on the experimentation as compared with the exact solutions. Numerical results are included to demonstrate the reliability and efficiency of the methods. Graphical representation of the obtained results reconfirms the potential of the suggested method. Keywords: Power series, nonlinear problems, boundary value problem, numerical simulatio
Energy management of three-dimensional minimum-time intercept
A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission
SoftIGA: soft isogeometric analysis
We extend the softFEM idea to isogeometric analysis (IGA) to reduce the
stiffness (consequently, the condition numbers) of the IGA discretized problem.
We refer to the resulting approximation technique as softIGA. We obtain the
resulting discretization by first removing the IGA spectral outliers to reduce
the system's stiffness. We then add high-order derivative-jump penalization
terms (with negative penalty parameters) to the standard IGA bilinear forms.
The penalty parameter seeks to minimize spectral/dispersion errors while
maintaining the coercivity of the bilinear form. We establish dispersion errors
for both outlier-free IGA (OF-IGA) and softIGA elements. We also derive
analytical eigenpairs for the resulting matrix eigenvalue problems and show
that the stiffness and condition numbers of the IGA systems significantly
improve (reduce). We prove a superconvergent result of order for
eigenvalues where characterizes the mesh size and specifies the order
of the B-spline basis functions. To illustrate the main idea and derive the
analytical results, we focus on uniform meshes in 1D and tensor-product meshes
in multiple dimensions. For the eigenfunctions, softIGA delivers the same
optimal convergence rates as the standard IGA approximation. Various numerical
examples demonstrate the advantages of softIGA over IGA
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