In this article, a collocation method for the problems where the second-order derivative is multiplied by a small perturbation parameter ϵ, the coefficient of the convection term vanishes at a point within the domain of ...

This paper is devoted to the numerical study of the boundary value problems for nonlinear singularly perturbed differential-difference equations with small delay. Quasilinearization process is used to linearize the nonlinear ...

We devise a spline-based numerical technique for a class of two-parameter singularly perturbed problems having discontinuous convection and source terms. The problem is discretized using the Crank–Nicolson formula in the ...

This paper deals with the singularly perturbed boundary value problem for a linear second order differential–difference equation of the convection–diffusion type with small delay parameter of whose solution has a boundary ...

A numerical method based on finite difference method with variable mesh is given for second order singularly perturbed self-adjoint two point boundary value problems. The original problem is reduced to its normal form and ...

A numerical scheme is constructed for the second-order parabolic partial differential equation with piecewise smooth initial data. The scheme comprises an orthogonal spline collocation strategy with the Rannacher time-marching. ...

In this article, we present a novel numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ (BBMB) equation using Atangana Baleanu Caputo (ABC) derivative. First, we apply a linearization ...

In this paper, a new approach is presented to investigate the time-fractional advection-dispersion equation that is extensively used to study transport processes. The present modified fractional derivative operator based ...

A numerical scheme is developed for parabolic singularly perturbed boundary value problems, including multiple boundary turning points at the left endpoint of the spatial direction. The highest order derivative of these ...

Based on the basis of B-spline functions an efficient numerical scheme on a piecewise-uniform mesh is suggested to approximate the solution of singularly perturbed problems with an integral boundary condition and having a ...