In this paper we consider a class of singularly perturbed delay differential equations of convection diffusion type with integral boundary condition. A finite difference scheme with an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical experiments support our theoretical results.

Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition

https://link.springer.com/content/pdf/10.1186/s42787-020-00076-6.pdf

Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition

A class of singularly perturbed parabolic delay differential equation with discontinuous data is solved numerically. Numerical scheme based on the upwind finite difference method is presented on a ...

An adaptive difference scheme for parabolic delay differential equation with discontinuous coefficients and interior layers

A class of third order singularly perturbed delay differential equations of convection diffusion type with integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

The present paper aims to carry out a new scheme for solving a type of singularly perturbed boundary value problem with a second order delay differential equation. Getting through the solution, we used Reproducing Kernel Hilbert Space (RKHS) method as an efficient approach to obtain the analytical solution for ordinary or partial differential equations that appear in vast areas of science and engineering. A key of this method is to keeping the continuous form of problems. Indeed, without discretizing the continuous problem, we change it to an equivalent iterative form and proving its convergence. Also, we will present a construction of the reproducing kernel in Hilbert space that satisfying the homogeneous nonlinear boundary conditions of the considered problem. Accuracy amount of absolute error with respect to different parameters of singularity has been studied for the performance of this method by solving several hardly nonlinear problems. Error estimation and convergence analysis show that the approximate results have uniform convergence to the continuous solutions.

Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay

In this paper, a fitted finite difference method on Shishkin mesh is suggested to solve a class of third order singularly perturbed boundary value problems for ordinary delay differential equations of convection-diffusion type. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method is almost first order. Numerical results are provided to illustrate the theoretical results.

Fitted Finite Difference Method for Third Order Singularly Perturbed Delay Differential Equations of Convection Diffusion Type

An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

/pdf/a-second-order-convergent-initial-value-method-for-2j4sxjbrl5.pdf

A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type

In this paper, an asymptotic numerical method based on a fitted finite difference scheme and the fourth-order Runge–Kutta method with piecewise cubic Hermite interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problems for third-order ordinary differential equations of convection diffusion type with a delay An error estimate is derived using the supremum norm and it is of almost first-order convergence A nonlinear problem is also solved using the Newton’s quasi linearization technique and the present asymptotic numerical method Numerical results are provided to illustrate the theoretical results

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

In this article we consider a delayed one dimensional transport equation. The method of lines with Runge-Kutta method is applied to solve the problem. It is proved that the present method is stable and convergence of order O ( ∆t + ¯ h 4 ) . Numerical examples are presented to illustrate the method presented in this article.

/pdf/method-of-lines-and-runge-kutta-method-for-solving-delayed-185u1cbp.pdf

R. Mahendran

Papers

Fitted Finite Difference Method for Third Order Singularly Perturbed Delay Differential Equations of Convection Diffusion Type

An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Method of lines and Runge-Kutta method for solving delayed one dimensional transport equation