A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient

Abstract

In this paper a standard numerical method with piecewise linear interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problem for second order ordinary delay differential equations with discontinuous convection coefficient and source term. An error estimate is derived by using the supremum norm and it is of almost first order convergence. Numerical results are provided to illustrate the theoretical results.

A class of finite difference schemes for singularly perturbed delay differential equations of second order

“…The maximum pointwise errors and rate of convergence are presented in Table 5 for different values of perturbation parameter ε . The numerical solution using the scheme (18) with ε = 10 −8 and N = 32 , is plotted in Proposed method E N 1.0957e-06 2.7599e-07 6.9258e-08 1.7347e-08…”

“…Subburayan and Ramanujam [16,17] developed an initial value method for singularly perturbed delay differential equations on Shishkin mesh. In [18], they proposed an asymptotic initial value method for singularly perturbed delay differential equations in which coefficient of convection-diffusion term is discontinuous.…”

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

“…In recent years, both mathematicians and physicists have devoted remarkable effort to the study of numerical solutions of singularly perturbed delay differential equations with discontinuous data and large delay parameter. For instance, in [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , the authors suggested different numerical methods for solving singularly perturbed ordinary differential equations with discontinuous coefficients and large delay parameter using fitting techniques. Mukherjee and Natesan [24] developed the implicit upwind finite difference scheme on Shishkin-type meshes for a class of singularly perturbed parabolic convection-diffusion problems exhibiting strong interior layers.…”

Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term

“…Among the recently conducted studies on time dependent large spatial delay di erential equations, some to mention are [8][9][10][11] but still, all these are reaction-di usion problems with smooth data. Nonetheless, there are numerical methods for singularly perturbed ordinary di erential equations with nonsmooth data (discontinuous source term and/or convection coe cient) using special piecewise uniform meshes; see [12][13][14][15][16] and references therein.…”