This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...

The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the Gauss-Kronrod scheme. An essential progress was made only recently, based on new bounds and as-ymptotic properties for the S...

In this paper, a symmetric Jacobi–Gauss collocation scheme is explored for both linear and nonlinear differential-algebraic equations (DAEs) of arbitrary index.After standard index reduction techniques, a type of Jacobi–Gauss collocation scheme with N knots is applied to differential part whereas another type of Jacobi–Gauss collocation scheme with N + 1 knots is applied to algebraic part of th...

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in L∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The L∞ uniform estimate and H−1 compactness are ...

We have recently considered decomposing a system of nonlinear equations by defining new variables corresponding to the intermediate results in the evaluation process. In that previous work, we applied both a derivative-free component solution process and an interval Gauss–Seidel method to the large, sparse system of equations so obtained. An analysis of the component solution process indicates ...

In recent years multigrid methods have been proven to be very e cient for solving large systems of linear equations resulting from the discretization of positive de nite di erential equations by either the nite di erence method or the h-version of the nite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which ar...

In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundar...

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and val...

A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the numbe...

We present a systematic discussion of algorithms to multiply a vector by a matrix expressed as the Kronecker product of sparse matrices, extending previous work in a unified notational framework. Then, we use our results to define new algorithms for the solution of large structured Markov models. In addition to a comprehensive overview of existing approaches, we give new results with respect to...