In this paper, a class of third order singularly perturbed boundary value problems with suitable boundary conditions is considered. The third order boundary value problem is transformed to asymptotically equivalent second order boundary value problem. This problem is solved efficiently by using fitted Numerov method. Linear and non-linear examples are solved to illustrate the method and relativ...

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new eeective procedure, based on coordinate stretching and the Che...

In this paper, homotopy perturbation method is applied to solve moving boundary and isoperimetric problems. This method does not depend upon a small parameter in the equation, homotopy is constructed with an imbedding parameter p, which is considered as a “small parameter”. Finally, we use combined homotopy perturbation method and Green’s function method for solving second order problems. Some ...

Wireless Backbone Networks (WBNs) equipped with Multi-Radio Multi-Channel (MRMC) configurations do experience power control problems such as the inter-channel and co-channel interference, high energy consumption at multiple queues and unscalable network connectivity. Such network problems can be conveniently modelled using the theory of queue perturbation in the multiple queue systems and also ...

We present an algorithm to compute the pseudospectral abscissa for a nonlinear eigenvalue problem. The algorithm relies on global under-estimator and over-estimator functions for the eigenvalue and singular value functions involved. These global models follow from eigenvalue perturbation theory. The algorithm has three particular features. First, it converges to the globally rightmost point of ...

We study a boundary perturbation problem for a one dimensional Schrödinger equation in which the potential has a regular singularity near the perturbed end point. We give the asymptotic behaviour of the eigenvalues under the perturbation. This problem arose out of the author’s studies of singular elliptic operators in higher dimensions and we illustrate this point with an example. The class of ...

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are...

In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Four types of basic spectral regularization methods such as Showalter’s, Tikhonov’s, Lardy’s and Lavrentiev’s are applied to approximate the solution by introducing another large (or small) parameter. Convergence of the regularized solutions to t...