MANAS KUMAR MAHALIK - Academia.edu (original) (raw)

Uploads

Papers by MANAS KUMAR MAHALIK

Research paper thumbnail of An efficient numerical method for singularly perturbed second order ordinary differential equation

In this paper an exponentially fitted finite difference method is presented for solving singularl... more In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that the proposed technique is of first order accurate and the error constant is independent of the perturbation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.

Research paper thumbnail of An Asymptotic Initial Value Method for Singular Perturbation Problems Using Grid Equidistribution

An initial value technique is presented to solve singularly perturbed two-point boundary value pr... more An initial value technique is presented to solve singularly perturbed two-point boundary value problem. Using the basic idea of WKB method, an approximation due to asymptotic expansion of the solution of the problem is constructed.Theoriginal problem is reduced to a combination of an initial value problem and a terminal value problem. The terminal value problem is solved by trapezoidal method and then the initial value problem is solved by backward Euler methodon an appropriate non-uniform mesh constructed adaptively by equidistributing a positive monitor function based on the solution. An error estimate is derived and numerical experiments are conducted to illustrate the efficiency of the proposed method.

Research paper thumbnail of An efficient numerical method for singularly perturbed second order ordinary differential equation

In this paper an exponentially fitted finite difference method is presented for solving singularl... more In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that the proposed technique is of first order accurate and the error constant is independent of the perturbation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.

Research paper thumbnail of An Asymptotic Initial Value Method for Singular Perturbation Problems Using Grid Equidistribution

An initial value technique is presented to solve singularly perturbed two-point boundary value pr... more An initial value technique is presented to solve singularly perturbed two-point boundary value problem. Using the basic idea of WKB method, an approximation due to asymptotic expansion of the solution of the problem is constructed.Theoriginal problem is reduced to a combination of an initial value problem and a terminal value problem. The terminal value problem is solved by trapezoidal method and then the initial value problem is solved by backward Euler methodon an appropriate non-uniform mesh constructed adaptively by equidistributing a positive monitor function based on the solution. An error estimate is derived and numerical experiments are conducted to illustrate the efficiency of the proposed method.

Log In