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

Abstract

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 thirdorder 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. Keywords Third-order differential equations • Convection diffusion equation • Boundary value problem • Singularly perturbed problem • Shishkin mesh • Delay differential equations • Asymptotic numerical methods Mathematics Subject Classification 34K10 • 34K26 • 34K28

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