@Article{Al-Mutib1984, author="A. N. Al-Mutib", title="Stability properties of numerical methods for solving delay differential equations", journal="J. Comput. Appl. Math.", year="1984", pages="71--79", volume="10" } @Article{Bainov1995, author="D. D. Bainov, Z. Kamont, E. Minchev", title="Comparison principles for impulsive hyperbolic equations of first order", journal="J. Comput. Appl. Math.", year="1995", pages="379--388", volume="60" } @Article{Banasiak1998, author="J. Banasiak, J. R. Mika", title="Singularly perturbed telegraph equations with applications in the random walk theory", journal="J. Appl. Math. Stochastic Anal.", year="1998", pages="9--28", volume="11" } @Book{Bellen2013, author="A. Bellen, M. Zennaro", title="Numerical methods for delay differential equations", year="2013", publisher="Oxford University Press", address="New York" } @Article{Feng2000, author="Z. L. Feng, H. R. Thieme", title="Endemic models with arbitrarily distributed periods of infection I: fundamental properties of the model", journal="SIAM J. Appl. Math.", year="2000", pages="803--833", volume="61" } @Book{Gopalsamy1992, author="K. Gopalsamy", title="Stability and Oscillations in Delay Differential Equations of Population Dynamics", year="1992", publisher="Kluwer Academic Publishers", address="Dordrecht" } @Book{Hairer1996, author="E. Hairer, G. Wanner", title="Solving ordinary differential equations II", year="1996", publisher="Springer", address="Berlin" } @Article{Hethcote1995, author="H. W. Hethcote, P. van den Driessche", title="An SIS epidemic model with variable population size and a delay", journal="J. Math. Biol.", year="1995", pages="177--194", volume="34" } @Article{Hethcote2000, author="H. W. Hethcote, P. van den Driessche", title="Two SIS epidemiologic models with delays", journal="J. Math. Biol.", year="2000", pages="3--26", volume="40" } @Book{Holden2013, author="A. V. Holden", title="Models of the stochastic activity of neurons", year="2013", publisher="Springer Science and Business Media", address="Berlin" } @Article{Karthick2021, author="S. Karthick, V. Subburayan", title="Finite Difference Methods with Interpolation for First-Order Hyperbolic Delay Differential Equations", journal="In: Differential equations and applications", year="2021", pages="147--161", volume="2021" } @Article{Karthick2022, author="S. Karthick, V. Subburayan, R. P. Agrwal", title="Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation", journal="Symmetry", year="2022", pages="18 pages", volume="14" } @Book{Kuang1993, author="Y. Kuang", title="Delay Differential Equations with applications in population dynamics", year="1993", publisher="Academic Press", address="San Diego" } @Book{Langtangen2017, author="H. P. Langtangen, S. Linge", title="Finite difference computing with PDEs: a modern software approach", year="2017", publisher="Springer", address="Cham" } @Book{Li2017, author="Z. Li, Z. Qiao, T. Tang", title="Numerical solution of differential equations: introduction to finite difference and finite element methods", year="2017", publisher="Cambridge University Press", address="Cambridge" } @Article{Liu1993, author="X.-D. Liu", title="A maximum principle satisfying modification of triangle based adapative stencils for the solution of scalar hyperbolic conservation laws", journal="SIAM J. Numer. Anal.", year="1993", pages="701--716", volume="30" } @Book{Loustau2016, author="J. Loustau", title="Numerical Differential Equations", year="2016", publisher="World Scientific", address="Hackensack" } @Book{Mazumder2015, author="S. Mazumder", title="Numerical methods for partial differential equations", year="2015", publisher="Elsevier/Academic Press", address="Amsterdam" } @Book{Miller1996, author="J. J. H. Miller, E. O’riordan, G. I. Shishkin", title="Fitted numerical methods for singular perturbation problems", year="1996", publisher="World scientific", address="New York" } @Book{Protter1967, author="M. H. Protter, H. F. Weinberger", title="Maximum principles in differential equations", year="1967", publisher="Prentice-Hall", address="Englewood Cliffs" } @Article{Rai2012, author="P. Rai, K. K. Sharma", title="Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability", journal="Comput. Math. Appl.", year="2012", pages="118--132", volume="63" } @Article{Rana2021, author="M. M. Rana, V. E. Howle, K. Long, A. Meek", title="A New Block Preconditioner for Implicit Runge–Kutta Methods for Parabolic PDE Problems", journal="SIAM J. Sci. Comput.,", year="2021", pages="475--495", volume="43" } @Article{Sharma2008, author="K. K. Sharma, P. Singh", title="Hyperbolic partial differential-difference equation in the mathematical modeling of neuronal firing and its numerical solution", journal="Appl. Math. Comput.", year="2008", pages="229--238", volume="201" } @Article{Singh2018, author="S. Singh, V. K. Patel, V. K. Singh", title="Application of wavelet collocation method for hyperbolic partial differential equations via matrices", journal="Appl. Math. Comput.", year="2018", pages="407--424", volume="320" } @Article{Singh2010, author="P. Singh, K. K. Sharma", title="Numerical solution of first-order hyperbolic partial differential-difference equation with shift", journal="Numer. Methods Partial Differential Equations", year="2010", pages="107--116", volume="26" } @Book{Smith1985, author="G. D. Smith", title="Numerical Solution of Partial Differential Equations: Finite Difference Methods", year="1985", publisher="Oxford University Press", address="New York" } @Book{Smith2011, author="H. Smith", title="An introduction to delay differential equations with applications to the life sciences", year="2011", publisher="Springer", address="New York" } @Article{Stein1965, author="R. B. Stein", title="A theoretical analysis of neuronal variability", journal="Biophys. J.", year="1965", pages="173--194", volume="5" } @Article{Stein1967, author="R. B. Stein", title="Some models of neuronal variability", journal="Biophys. J.", year="1967", pages="37--68", volume="7" } @Book{Strikwerda2004, author="J. C. Strikwerda", title="Finite difference schemes and partial differential equations", year="2004", publisher="SIAM", address="Philadelphia" } @Article{Subburayan2013, author="V. Subburayan, N. Ramanujam", title="An asymptotic numerical method for singularly perturbed convection-diffusion problems with a negative shift", journal="Neural Parallel Sci. Comput.", year="2013", pages="431--446", volume="21" } @Article{Subburayan2013, author="V. Subburayan, N. Ramanujam", title="An initial value technique for singularly perturbed convection-diffusion problems with a negative shift", journal="J. Optim. Theory Appl.", year="2013", pages="234--250", volume="158" } @Book{Suli2003, author="E. Suli, D. F. Mayers", title="An introduction to numerical analysis", year="2003", publisher="Cambridge university press", address="Cambridge" } @Article{Takei2022, author="Y. Takei, Y. Iwata", title="Numerical Scheme Based on the Implicit Runge-Kutta Method and Spectral Method for Calculating Nonlinear Hyperbolic Evolution Equations", journal="Axioms", year="2022", pages="19 pages", volume="11" } @Article{Warming1974, author="R. F. Warming, B. J. Hyett", title="The modified equation approach to the stability and accuracy analysis of finite-difference methods", journal="J. Comput. phys.", year="1974", pages="159--179", volume="14" }