Papers by Mohan Kadalbajo
Applied Mathematics and Computation, 1993
Third-order variable-mesh methods based on cubic spline approximation for nonlinear singularly pe... more Third-order variable-mesh methods based on cubic spline approximation for nonlinear singularly perturbed boundary-value problems of the form vu =f(x, y), y(u) = a, y(b) = p are presented. The convergence analysis is given and the method is shown to have third-order convergence. Several test examples are solved to demonstrate the efficiency of the method. 1.
Applied Mathematics and Computation, 2002
ABSTRACT Some difference schemes for singularly perturbed two-point boundary value problems are d... more ABSTRACT Some difference schemes for singularly perturbed two-point boundary value problems are derived using spline in tension. These schemes are second-order accurate. Numerical examples are given in support of the theoretical results.
Boundary value problems for singularly perturbed differential difference equations containing del... more Boundary value problems for singularly perturbed differential difference equations containing delay with layer behavior are considered. There are a number of realistic models in the literature where one encounters BVPs for singularly perturbed differential difference equations with small delay, such as in variational problems in control theory and first exit time problems in modeling of activation of neurons. In some recent papers, the terms negative shift for ‘delay’ and positive shift for ‘advance’ are used. In this paper, a numerical method based on the fitted mesh approach to approximate the solution of these types of boundary value problems is presented. In this method the piecewise-uniform meshes are constructed and fitted to the boundary layer regions to adapt singular behavior of the operator in these narrow regions. Both the cases, layer on the left side boundary and layer on the right side boundary, are discussed. It is shown that the method composed of an upwind differenc...
arXiv: Numerical Analysis, 2006
A general procedure to construct a class of simple and efficient high resolution Total Variation ... more A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy satisfying first order accurate scheme and second order accurate upstream scheme using the flux limiter function. The obtained high resolution schemes are shown to be TVD for 1-D scalar case. Bounds for the limiter function are given. Numerical experiments for various test problems clearly show that the resulting schemes give entropy consistent solution with higher resolution as compared to their corresponding first order schemes.
This paper sketches the research developments in the area of computational methods for solving th... more This paper sketches the research developments in the area of computational methods for solving the eigenvalue problems and how the methods developed relate to each other as they evolve over centuries. This is an attempt to write a complete overview on the research on computational aspects of eigenvalue problem, emphasize the history of methods that still play a role and some of those that no longer are considered to be on the main track but are somehow related to the present techniques in some smaller steps. This contribution brings out the state-of-the-art of the algorithms for solving large-scale eigenvalue problems for both symmetric and nonsymmetric matrices separately, thereby clearly drawing a comparison between the differences in the algorithms in practical use for the two. Some of the methods or modifications to the earlier methods that have been notable at the turn of the 21st century will also be covered through this paper under "Modem Approaches". Also as the st...
International Journal of Computer Mathematics, 2003
ABSTRACT In this paper, an ϵ-uniform fitted operator method which solves boundary-value problems ... more ABSTRACT In this paper, an ϵ-uniform fitted operator method which solves boundary-value problems for singularly perturbed differential-difference equations containing small delay with boundary layer behavior is presented. Both the cases, i.e., when boundary layer is on the left side and when boundary layer is on the right side are discussed here. It is shown that the scheme is ϵ-uniform by establishing the error estimate. The effect of small delay on the boundary layer solution is shown by considering several numerical experiments. Numerical results in terms of maximum errors are tabulated and plots giving computed and exact solution demonstrate the efficiency of the method.
International Journal of Computer Mathematics, 2004
ABSTRACT The boundary-value problems (BVPs) for singularly perturbed nonlinear delay differential... more ABSTRACT The boundary-value problems (BVPs) for singularly perturbed nonlinear delay differential equations are studied. In this article, we present a parameter uniform numerical scheme based on the fitting mesh technique in the boundary layer region to solve such BVPs. To tackle the nonlinearity, we use the quasilinearization process [1], and to handle the delay term, we use the Taylor series [2]. In the limit, the solution of the linear BVPs obtained after quasilinearization converges quadratically to the solution of the nonlinear BVP for a judicious initial approximation. The sequence of linear problems so obtained after quasilinearization is analyzed for convergence, and error estimates for the solution of the discretized problem are derived. The method is compared with a standard upwind difference scheme and fitted operator method on uniform mesh by carrying out several numerical experiments.E-mail: [email protected]
Journal of Mathematical Analysis and …, 2009
This paper is concerned with a numerical scheme to solve a singularly perturbed convection–diffus... more This paper is concerned with a numerical scheme to solve a singularly perturbed convection–diffusion problem. The solution of this problem exhibits the boundary layer on the right-hand side of the domain due to the presence of singular perturbation parameter ε. The scheme ...
Journal of Computational and …, 2008
A numerical method is proposed for solving singularly perturbed one-dimensional parabolic convect... more A numerical method is proposed for solving singularly perturbed one-dimensional parabolic convection–diffusion problems. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and B-...
Computers & Mathematics with Applications, 2001
A numerical method based on cubic spline with nonuniform grid is given for the singularly perturb... more A numerical method based on cubic spline with nonuniform grid is given for the singularly perturbed two-point boundary value problems having turning point. The scheme derived in this paper is second-order accurate. Numerical examples are given to support the predicted theory.
Computers & Mathematics With Applications - COMPUT MATH APPL, 2001
A numerical method based on cubic spline with nonuniform grid is given for the singularly perturb... more A numerical method based on cubic spline with nonuniform grid is given for the singularly perturbed two-point boundary value problems having turning point. The scheme derived in this paper is second-order accurate. Numerical examples are given to support the predicted theory.
Applied Mathematics and Computation, 2008
In this paper we have considered an important class of time-dependent singularly perturbed convec... more In this paper we have considered an important class of time-dependent singularly perturbed convection-diffusion problems with retarded terms which often arise in Computational Neuroscience. We used Taylors series to approximate the retarded terms and the resulting time-dependent singularly perturbed differential equation is approximated using parameters uniform numerical methods based on Euler implicit, upwind and midpoint upwind finite difference schemes. We discretize the continuous problem using implicit Euler scheme in the time direction with a constant step size and the resulting system of equations is approximated using upwind and midpoint upwind difference schemes on a piecewise uniform mesh. We will prove the uniform convergence of these two schemes. Numerical experiments support the convergence results.
Applied Mathematical Modelling, 2010
In this paper, we have presented a computational method for solving singularly perturbed delay di... more In this paper, we have presented a computational method for solving singularly perturbed delay differential equations with twin layers or oscillatory behaviour. In this method, the original second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, we have employed numerical integration and linear interpolation to get tridiagonal system. This tridiagonal system is solved efficiently by using discrete invariant imbedding algorithm. Several model examples are solved, and computational results are presented by taking various values of the delay parameter and perturbation parameter. We have also discussed the convergence of the method.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Computer Mathematics, 1994
A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for th... more A direct parallel method, called new quadrant interlocking factorization (Q. I. F.) method for the solution of tridiagonallinear systems is given by Chawla and Passi [1]. Kadalbajoo et al. [2] showed that the nonsingularity of the tridiagonal matrix is not the sufficient condition for the existence of Q. I. F. method and they proved the existence of the Q. I.
International Journal of Parallel, Emergent and Distributed Systems, 2000
A direct parallel method called Alternate Quadrant Interlocking Factorization (AQIF); A = WZ, is ... more A direct parallel method called Alternate Quadrant Interlocking Factorization (AQIF); A = WZ, is introduced (Rao, Parallel Algorithms and Applications, 4, 1-20, 1994) for the general solution of the linear system Ax = b. The matrices W and Z are closed under multiplication and inversion. In this paper AQIF is used with partition method for the solution of the banded
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Papers by Mohan Kadalbajo