Rajesh K. Bawa

An ϵ-uniform hybrid scheme for singularly perturbed delay differential equations

In this paper, a singularly perturbed delay differential equation of first order has been considered. The problem is solved by using a hybrid scheme on a Shishkin mesh. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Truncation errors are obtained. Finally, numerical experiments are carried out on a test problem, confirming the effectiveness of the proposed technique.

A Preprocessing Technique for Recognition of Online Handwritten Gurmukhi Numerals

In this paper, a preprocessing technique involving removal of duplicate points, normalization, interpolation of missing points, sharp point detection, removing hook and smoothing is applied for recognition of online handwritten Gurmukhi numerals. Above stages are performed on the data collected from different persons. It is observed that our preprocessing technique improves feature extraction rate by increasing the accuracy in recognition of some features like hole and junction.

Higher order global solution and normalized flux for singularly perturbed reaction-diffusion problems

In this paper a computational technique is proposed for obtaining a higher order global solution and global normalized flux of singularly perturbed reaction-diffusion two-point boundary-value problems. The HOC (higher order compact) finite difference scheme developed in Gracia et al. (2001) [4] and which is constructed on an appropriate piecewise uniform Shishkin mesh, has been considered to find an almost fourth order convergent solution at mesh points. Using these values, piecewise cubic interpolants based approximations for solution and normalized flux in whole domain have been defined. It has been shown that the global solution and the global normalized flux are also uniformly convergent. Moreover, for the global solution, the order of uniform convergence in the whole domain is optimal, i.e., it is the same as this one obtained at mesh points, whereas, for the global normalized flux, the uniform convergence is almost third order, except at midpoints of the mesh, where it is also almost fourth order. Theoretical error bounds have been provided along with some numerical examples, which corroborate the efficiency of the proposed technique to find good approximations to the global solution and the global normalized flux.

A robust second-order numerical method for global solution and global normalized flux of singularly perturbed self-adjoint boundary-value problems

In this paper, we consider the finite difference hybrid scheme constructed by Natesan et al. for obtaining uniformly convergent global solution and uniformly convergent normalized flux for self-adjoint singularly perturbed boundary value problems. The global solution is obtained from the numerical solution at the mesh points of this scheme, having almost second-order uniform convergence at the nodal points when it is constructed on a piecewise uniform Shishkin mesh. Using a classical cubic spline, we define the solution and the normalized flux on the entire domain. We prove that the uniform order of convergence of the global solution is the same as that of the hybrid scheme at the mesh points. In addition, the global normalized flux is also almost second-order uniformly convergent in the whole domain. We provide theoretical error bounds and some numerical examples showing the efficiency of the proposed technique for obtaining the global solution and the normalized flux.

A review on binarization algorithms for camera based natural scene images

Text Information Extraction is a system that receives input in the form of a still image or a sequence of images and the output is only text part of the image, which is recognized by Optical character recognition (OCR). The problem of TIE can be divided into following sub-problems: (i) Text detection (ii) Text localization (iii) Text extraction and enhancement, and(iv)Text recognition. For the purpose of extracting text input image has to be binarized so as to make the recognition of text possible. In present paper several global and local image thresholding algorithms are reviewed for binarizing camera based natural scene(NS) images containing text.

An efficient hybrid numerical scheme for convection-dominated boundary-value problems

This article presents a numerical scheme for convection-dominated two-point boundary-value problems. The proposed scheme combines the cubic spline scheme and the midpoint scheme in an appropriate manner. In the inner region, the convective term is approximated by three-point differences by spline approximation of solution at the mesh points, whereas in the outer region the midpoint approximations are used for convective term, and the classical central difference scheme is used for the diffusive term. The first-order derivative in the left boundary point is approximated by the cubic spline. This scheme is applied on the boundary layer resolving Shishkin mesh. Truncation error is derived, and the proposed method is applied to couple of examples to show its accuracy and efficiency.

Parallelizable computational technique for singularly perturbed boundary value problems using spline

In this paper, we considered singularly perturbed self–adjoint boundary-value problems and proposed a computational technique based on spline scheme, which is also suitable for parallel computing. The whole domain is divided into three non-overlapping subdomains and corresponding subproblems are obtained by using zeroth order approximations of the solution at boundaries of these subproblems. The subproblems corresponding to boundary layer regions are solved using adaptive spline scheme. Numerical example is provided to show the efficiency and accuracy. Subject Classification: AMS 65L10 CR G1.7.

Parallel Implementation of a Spline Based Computational Approach for Singular Perturbation Problems

In this paper, a parallelizable computational technique for singularly perturbed reaction-diffusion problems is analyzed and implemented on parallel computer. In this technique, the domain is decomposed into non-overlapping subdomains, and boundary value problems are posed on each subdomain with suitable boundary conditions. Then, each problem is solved by the adaptive spline based difference scheme on each subinterval on parallel computer. Detailed theoretical analysis is provided to prove the convergence of the technique. To check the validity of the method, parallel implementation is performed on a numerical example and results are presented.

An Efficient Computational Technique for a System of Singularly Perturbed Initial Value Problems

In this paper, a parameter-uniformly convergent computational technique for a system of singularly perturbed initial value problems, which is applied on a piecewise uniform Shishkin mesh is presented. Numerical experiments are carried out on some test problems which shows almost second order uniform convergence, confirming the efficiency of the proposed technique.

A parallel approach for self-adjoint singular perturbation problems using Numerov's scheme

In this paper, we considered singularly perturbed self-adjoint boundary-value problems and proposed a computational technique based on Numerovs scheme, which is also suitable for parallel computing. The whole domain is divided into three non-overlapping subdomains, and corresponding subproblems are obtained by using zeroth-order approximations of the solution at the boundaries of these subproblems. The subproblems corresponding to boundary-layer regions are solved using Numerovs method after the introduction of suitable stretching variables and the solution of the reduced problem is taken as an approximate solution in the outer region. A numerical example is provided to show the efficiency and accuracy of the technique.