A singularly perturbed Volterra integro-differential equation with an integrable singularity in the integral term is considered. The upwind difference method is used to discretize the singularly perturbed Volterra integro-differential equation. ...

In this work, we consider an optimal accurate numerical approximation for the boundary layer adaptive solution of a system of reaction–diffusion problems involving a small perturbation parameter. To generate the layer adaptive mesh, we ...

This paper discusses the numerical solution of linear 1-D singularly perturbed parabolic convection-diffusion-reaction problems with two small parameters using a moving mesh-adaptive algorithm which adapts meshes to boundary layers. The meshes are ...

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving ...

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used ...

This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional Q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by ...

A generalization is given for a characterization of the spectral density function of Weyl and Titchmarsh for a singular Sturm-Liouville problem having absolutely continuous spectrum in [0,~). A recurrent formulation is derived that generates a family of ...

Algorithms for computing Sturm-Liouville spectral density functions are developed based on several mathematical characterizations. Convergence and error bounds are derived and methods are tested on several examples. The results are compared with those ...