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This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed convection–diffusion equations. The well-known dual-weighted residual (DWR) technique has been adopted to elevate the accuracy of the error estimator. Our main contribution is finding an efficient computable DWR-type robust residual-based a posteriori error bound for the SDFEM. The local lower error bound has also been provided. An adaptive mesh refinement algorithm has been addressed and lastly, some numerical experiments are carried out to justify the theoretical proofs. [ABSTRACT FROM AUTHOR]

In this article, we study the convergence of the streamline-diffusion finite element method (SDFEM) for singularly perturbed boundary-value problem with two parameters. We prove that the SDFEM is uniformly convergent in the discrete SD-norm, of second-order on the Shishkin mesh and almost second-order on the Duran–Shishkin mesh. Numerical results are presented to support the theoretical error estimates. [ABSTRACT FROM AUTHOR]

A new C1-rational cubic fractal interpolation surface is introduced to interpolate the surface data which lies on a rectangular grid. At the beginning, C1-rational cubic fractal interpolation functions are constructed along the grid lines. Then, the C1-rational cubic fractal interpolation surface is constructed with the help of blending functions and the rational cubic fractal interpolation functions. Convergence analysis of the fractal interpolation surface to an original function is carried out. Further, the scaling factors and the shape parameters are constrained, so that the fractal interpolation surface would lie above the fixed plane whenever the surface data lie above the plane. Also, conditions on the scaling factors and the shape parameters are derived to interpolate the convex surface data. [ABSTRACT FROM AUTHOR]

In this article, we study the numerical solution of singularly perturbed non-linear autonomous initial-value problems by a non-standard algorithm on layer-resolving nonuniform meshes. Here, we use the piecewise-uniform Shishkin meshes, and two other nonuniform meshes which resolve the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem without linearization and provides third-order convergence results. Linear stability of this method is studied. Numerical experiments are carried out to verify the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

Synthetic fibers made from nylon or polypropylene have gained application when loose and woven into geo textile form although no information on the matrix’s mechanical performance is obtained so that more understanding of their structural contribution to resist cracking can be determined. This paper presents the results of an experimental investigation to determine the performance characteristics of concrete reinforced with a polypropylene structural fiber. In this investigation “Fiber mesh” brand of fibers manufactured by SL Concrete System, Tennessee, USA and marketed by M/S Millennium Building System, Inc., Bangalore, India are used. The lengths of the fibers used were 24 mm. Fiber dosages used were 0.9, 1.8, 2.7 kg/m3. A total of three mixtures, one for each fiber dosage were made. A standard slump cone test was conducted on the fresh concrete mix with and without fibers to determine the workability of the mix. The test program included the evaluation of hardened concrete properties such as compressive, split tensile, modulus of rupture and flexural strengths. The increase in compressive strength is about 36.25%, 26.20%, and 23.75% respectively that of plain concrete. This increase in strength was directly proportional to amount of fibers present in the mix. The increase in flexural strength for Mixes I∼III is about 21%, 16.6%, and 23% respectively that of plain concrete specimens. An experimental investigation was also made to study the behaviors of reinforced fibers concrete beams (with longitudinal reinforcements) under two-point loading. The deflection and crack patterns were also studied. The improvements in strength and ductility characteristics were discussed. [ABSTRACT FROM AUTHOR]

A robust numerical method for a singularly perturbed secondorder ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations. [ABSTRACT FROM AUTHOR]

A class of singularly perturbed two-point boundary-value problems (BVPs) for second-order ordinary differential equations (DEs) is considered here. In order to obtain numerical solution to these problems, an iterative non-overlapping domain decomposition method is suggested. The BVPs are independent in each subdomain and one can use parallel computers to solve these BVPs. One of the characteristics of the method is that the number of processors available is a free parameter of the method. Practical experiments on a Silicon Graphics Origin 200, with 4 MIPS R10000 processors have been performed, showing the reliability and performance of the proposed parallel schemes. Error estimates for the solution and numerical examples are provided. [ABSTRACT FROM AUTHOR]

A numerical method for singularly-perturbed self-adjoint boundary-value problems for second-order ordinary differential equations subject to Neumann boundary conditions is proposed. In this method (booster method), an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived for this method when implemented in known difference schemes. Numerical examples are presented to illustrate the present method. [ABSTRACT FROM AUTHOR]

An improved numerical method for singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations subject to Neumann-type boundary conditions is proposed. In this method, an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived when implemented in known difference schemes. Numerical results are presented in support of the proposed method. [ABSTRACT FROM AUTHOR]

The initial-value technique that was originally developed for solving singularly-perturbed nonturning-point problems (Ref. 1) is used here to solve singularly-perturbed turning-point problems exhibiting twin boundary layers. In this method, the required approximate solution is obtained by combining solutions of the reduced problem, an initial-value problem, and a terminal-value problem. Error estimates for approximate solutions are obtained. The implementation of the method on parallel architectures is discussed. Numerical examples are presented to illustrate the present technique. [ABSTRACT FROM AUTHOR]

An initial-value technique is presented for solving singularly perturbed two-point boundary-value problems for linear and semilinear second-order ordinary differential equations arising in chemical reactor theory. In this technique, the required approximate solution is obtained by combining solutions of two terminal-value problems and one initial-value problem which are obtained from the original boundary-value problem through asymptotic expansion procedures. Error estimates for approximate solutions are obtained. Numerical examples are presented to illustrate the present technique. [ABSTRACT FROM AUTHOR]

In this article, we study the convergence properties of the streamline-diffusion finite element method (SDFEM) for singularly perturbed 1D parabolic convection–diffusion initial-boundary-value problems. To discretize the spatial domain, we use a layer-adaptive nonuniform grids obtained through the equidistribution principle, whereas uniform grid is used in the time direction. Here, we use the backward-Euler method to discretize the temporal derivative and the SDFEM scheme for the spatial derivatives. The proposed method is uniformly convergent with first-order in time and second-order in space. [ABSTRACT FROM AUTHOR]

In this article, a new α -fractal rational cubic spline is introduced with the help of the iterated function system (IFS) that contains rational functions. The numerator of the rational function contains a cubic polynomial and the denominator of the rational function contains a quadratic polynomial with three shape parameters. The convergence analysis of the α -fractal rational cubic spline is established. By restricting the scaling factors and the shape parameters, the α -fractal rational cubic spline is constrained between two piecewise linear functions whenever interpolation data lies in between two piecewise linear functions. Also, positivity and monotonicity of the α -fractal rational cubic spline are discussed. Numerical examples are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Ornithine carbamoyltransferase (OCT) and arginase, but not arginine synthetase (AS), were detected in the body wall and gut tissues of the leech. The activities of these enzymes were not altered by starvation. The high activity of arginase in body wall is probably due to the association of the latter with botryoidal tissue. Hirudineans, which evolved from oligochaete ancestors, appear to have lost the citrulline-arginine segment of the urea cycle due to their ammonotelic mode of nitrogen excretion. [ABSTRACT FROM AUTHOR]