%0 Journal Article %T A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type %A Senthilkumar, L. S. %A Mahendran, R. %A Subburayan, V. %J Journal of Mathematics and Computer Science %D 2022 %V 25 %N 1 %@ ISSN 2008-949X %F Senthilkumar2022 %X In this article, a system of second order singularly perturbed delay differential equations of convection diffusion type problem is considered. An asymptotic expansion approximation of the solution is constructed. Further the asymptotic expansion approximation is numerically approximated using the Runge Kutta methods and hybrid finite difference methods. The error estimate is obtained and it is of almost second order. Numerical examples are given to illustrate the present method. %9 journal article %R 10.22436/jmcs.025.01.06 %U http://dx.doi.org/10.22436/jmcs.025.01.06 %P 73--83 %0 Journal Article %T Finite-difference methods for boundary-value problems of differential equations with deviating arguments %A R. P. Agarwal %A Y. M. Chow %J Comput. Math. Appl. Ser. A %D 1986 %V 12 %F Agarwal1986 %0 Journal Article %T Numerical method for a singularly perturbed convection-diffusion problem with delay %A G. M. Amiraliyev %A C. Cimen %J Appl. Math. Comput. %D 2010 %V 216 %F Amiraliyev2010 %0 Journal Article %T Fitted mesh method for a weakly coupled system ofsingularly perturbed reaction-convectiondiffusion problems with discontinuous source term %A P. M. Basha %A V. Shanthi %J Ain Shams Eng. J. %D 2018 %V 9 %F Basha2018 %0 Journal Article %T Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations %A Z. Cen %J Int. J. Comput. Math %D 2005 %V 82 %F Cen2005 %0 Journal Article %T A hybrid finite difference scheme for a class of singularly perturbed delay differential equations %A Z. Cen %J Neural Parallel Sci. Comput. %D 2008 %V 16 %F Cen2008 %0 Journal Article %T A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems %A Z. Cen %A A. Xu %A A. Le %J J. Comput. Appl. Math. %D 2010 %V 234 %F Cen2010 %0 Journal Article %T A uniformly convergent hybrid difference scheme for a system of singularly perturbed initial value problems %A Z. Cen %A A. Xu %A A. Le %A L.-B. Liu %J Int. J. Comput. Math. %D 2020 %V 97 %F Cen2020 %0 Journal Article %T An almost third order finite difference scheme for singularly perturbed reactiondiffusion systems %A C. Clavero %A J. L. Gracia %A F. J. Lisbona %J J. Comput. Appl. Math. %D 2010 %V 234 %F Clavero2010 %0 Journal Article %T Asymptotic analysis and solution of a finite-horizon $H_\infty$ control problem for singularly-perturbed linear systems with small state delay %A V. Y. Glizer %J J. Optim. Theory Appl. %D 2003 %V 117 %F Glizer2003 %0 Journal Article %T A stage structured predator-prey model and its dependence on maturation delay and death rate %A S. A. Gourley %A Y. Kuang %J J. Math. Biol. %D 2004 %V 49 %F Gourley2004 %0 Journal Article %T Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations %A M. K. Kadalbajoo %A K. K. Sharma %J Comput. Appl. Math. %D 2005 %V 24 %F Kadalbajoo2005 %0 Journal Article %T Singular perturbation analysis of boundary value problems for differential-difference equations. V. Small shifts with layer behavior %A C. G. Lange %A R. M. Miura %J SIAM J. APPL. MATH. %D 1994 %V 54 %F Lange1994 %0 Journal Article %T Complex oscillations in the human pupil light reflex with “mixed” and delayed feedback %A A. Longtin %A J. G. Milton %J Math. Biosci. %D 1988 %V 90 %F Longtin1988 %0 Journal Article %T A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems %A N. Madden %A M. Stynes %J IMA J. Numer. Anal., %D 2003 %V 23 %F Madden2003 %0 Journal Article %T A parameter-uniform first order convergent numerical method for a system of singularly perturbed second order delay differential equations %A M. Mariappan %A J. J. H. Miller %A V. Sigamani %J Boundary and interior layers, computational and asymptotic methods–BAIL 2014, Springer, Cham %D 2015 %V 108 %F Mariappan2015 %0 Journal Article %T A numerical method for a system of singularly perturbed reaction–diffusion equations %A S. Matthews %A E. O’Riordan %A G. I. Shishkin %J J. Comput. Appl. Math. %D 2002 %V 145 %F Matthews2002 %0 Journal Article %T Solving systems of singularly perturbed convection diffusion problems via initial value method %A W. G. Melesse %A A. A. Tiruneh %A G. A. Derese %J J. Appl. Math. %D 2020 %V 2020 %F Melesse2020 %0 Journal Article %T Uniform convergence analysis of finite difference scheme for singularly perturbed delay differential equation on an adaptively generated grid %A J. Mohapatra %A S. Natesan %J Numer. Math. Theory Methods Appl. %D 2010 %V 3 %F Mohapatra2010 %0 Journal Article %T A new algorithm appropriate for solving singular and singularly perturbed autonomous initialvalue problems %A H. Ramos %A J. Vigo-Aguiar %J Int. J. Comput. Math. %D 2008 %V 85 %F Ramos2008 %0 Journal Article %T An improved initial value method for singularly perturbed convection diffusion delay differential equations %A L. S. Senthilkumar %A V. Subburayan %J Adv. Math., Sci. J. %D 2021 %V 10 %F Senthilkumar2021 %0 Journal Article %T Asymptotic initial value technique for singularly perturbed convection–diffusion delay problems with boundary and weak interior layers %A V. Subburayan %A N. Ramanujam %J Appl. Math. Lett. %D 2012 %V 25 %F Subburayan2012 %0 Journal Article %T An initial value technique for singularly perturbed convection-diffusion problems with a negative shift %A V. Subburayan %A N. Ramanujam %J J. Optim. Theory Appl. %D 2013 %V 158 %F Subburayan2013 %0 Journal Article %T An asymptotic numerical method for singularly perturbed convection-diffusion problems with a negative shift %A V. Subburayan %A N. Ramanujam %J Neural Parallel Sci. Comput. %D 2013 %V 21 %F Subburayan2013 %0 Journal Article %T An asymptotic numerical method for singularly perturbed weakly coupled system of convection-diffusion type differential equations %A V. Subburayan %A N. Ramanujam %J Novi Sad J. Math. %D 2014 %V 44 %F Subburayan2014 %0 Journal Article %T Uniformly convergent finite difference schemes for singularly perturbed convection diffusion type delay differential equations %A V. Subburayan %A N. Ramanujam %J Differ. Equ. Dyn. Syst. %D 2021 %V 29 %F Subburayan2021 %0 Journal Article %T A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term %A A. Tamilselvan %A N. Ramanujam %A V. Shanthi %J J. Comput. Appl. Math. %D 2007 %V 202 %F Tamilselvan2007 %0 Book %T Introduction to theoretical neurobiology. Vol. 1 %A H. C. Tuckwell %D 1988 %I Cambridge University Press %C Cambridge %F Tuckwell1988 %0 Journal Article %T A parallel boundary value technique for singularly perturbed two-point boundary value problems %A J. Vigo-Aguiar %A S. Natesan %J J. Supercomput. %D 2004 %V 27 %F Vigo-Aguiar2004