Exponentially fitted non-polynomial cubic spline method for time-fractional singularly perturbed convection-diffusion problems involving large temporal lag.

Objective: The main purpose of this work is to present an exponentially fitted non-polynomial cubic spline method for solving time-fractional singularly perturbed convection-diffusion problem involving large temporal lag.

Result: The time-fractional derivative is considered in the Caputo sense and discretized using backward Euler technique. Then, on uniform mesh discretization, a non-polynomial cubic spline scheme is constructed along the spatial direction.

Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction-diffusion problems.

Objective: The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction-diffusion problem to produce more accurate solutions.

Results: Quasilinearization technique is used to linearize the semilinear term. The scheme is formulated with discretizing the solution domain piecewise uniformly and then replacing the differential equation by finite difference approximations.

Graded mesh B-spline collocation method for two parameters singularly perturbed boundary value problems.

The solutions of two parameters singularly perturbed boundary value problems typically exhibit two boundary layers. Because of the presence of these layers standard numerical methods fail to give accurate approximations. This paper introduces a numerical treatment of a class of two parameters singularly perturbed boundary value problems whose solution exhibits boundary layer phenomena.

A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift.

Objective: The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically.

A uniformly convergent numerical scheme for solving singularly perturbed differential equations with large spatial delay.

In this study, a parameter-uniform numerical scheme is built and analyzed to treat a singularly perturbed parabolic differential equation involving large spatial delay. The solution of the considered problem has two strong boundary layers due to the effect of the perturbation parameter, and the large delay causes a strong interior layer. The behavior of the layers makes it difficult to solve such problem analytically.

Uniformly convergent computational method for singularly perturbed unsteady burger-huxley equation.

This paper deals with the numerical treatment of a singularly perturbed unsteady non-linear Burger-Huxley problem. Due to the simultaneous presence of a singular perturbation parameter and non-linearity in the problem applying classical numerical methods to solve this problem on a uniform mesh are unable to provide oscillation-free results unless they are applied with very fine meshes inside the region. Thus, to resolve this issue, a uniformly convergent computational scheme is proposed.

Fitted computational method for solving singularly perturbed small time lag problem.

Objectives: An accurate exponentially fitted numerical method is developed to solve the singularly perturbed time lag problem. The solution to the problem exhibits a boundary layer as the perturbation parameter approaches zero. A priori bounds and properties of the continuous solution are discussed.

Computational method for singularly perturbed parabolic differential equations with discontinuous coefficients and large delay.

This paper deals with the computational method for a class of second-order singularly perturbed parabolic differential equations with discontinuous coefficients involving large negative shift. The formulated method comprises the implicit Euler and the cubic-spline in compression methods for time and spatial dimensions, respectively. Intensive numerical experimentation has been done on some model examples and the results are tabulated.

Second-order robust finite difference method for singularly perturbed Burgers' equation.

In this paper, a second-order robust method for solving singularly perturbed Burgers' equation were presented. To find the numerical approximation, we apply the quasilinearization technique before formulation of the scheme. The obtained experimental results show that the presented method has better numerical accuracy and convergence as compared to some existing methods in the literature.

Linear B-spline finite element method for the generalized diffusion equation with delay.

Objectives: The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson.

Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations.

Objective: The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions.

Results: The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically.

Accurate numerical scheme for singularly perturbed parabolic delay differential equation.

Objectives: Numerical treatment of singularly perturbed parabolic delay differential equation is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for numerical computation. Accurate numerical scheme is proposed using [Formula: see text]-method in time discretization and non-standard finite difference method in space discretization.

Novel approach to solve singularly perturbed boundary value problems with negative shift parameter.

Singularly perturbed boundary value problems with negative shift parameter are special types of differential difference equations whose solution exhibits boundary layer behaviour. A simple but novel numerical method is developed to approximate the numerical solution of the problems of these types. The method gives accurate solutions for in the inner region of the boundary layer where other classical numerical methods fail to give smooth solution.

Analysis of Atangana-Baleanu fractional-order SEAIR epidemic model with optimal control.

We consider a SEAIR epidemic model with Atangana-Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower.

Optimal control and sensitivity analysis for transmission dynamics of Coronavirus.

Analysis of mathematical models designed for COVID-19 results in several important outputs that may help stakeholders to answer disease control policy questions. A mathematical model for COVID-19 is developed and equilibrium points are shown to be locally and globally stable. Sensitivity analysis of the basic reproductive number (R) showed that the rate of transmission from asymptomatically infected cases to susceptible cases is the most sensitive parameter.

Extended cubic B-spline collocation method for singularly perturbed parabolic differential-difference equation arising in computational neuroscience.

A parameter uniform numerical method is presented for solving singularly perturbed parabolic differential-difference equations with small shift arguments in the reaction terms arising in computational neuroscience. To approximate the terms with the shift arguments, Taylor's series expansion is used. The resulting singularly perturbed parabolic differential equation is solved by applying the implicit Euler method in temporal direction and extended cubic B-spline basis functions consisting of a free parameter λ for the resulting system of ordinary differential equations in the spatial direction.