Stability and Accuracy Analysis of $$\theta $$ Scheme for a Convolutional Integro-Differential Equation

Atkinson, Kendall, Han, Weimin: Theoretical numerical analysis. Springer, New York (2009)

Bates, Peter, Chen, Fengxin: Periodic travelling waves for a nonlocal integro-differential model. Electron. J. Differ. Equ. 1999(26), 1–19 (1999)

Bates, Peter W., Chmaj, Adam: A discrete convolution model for phase transitions. Arch. Ration. Mech. Anal. 150(4), 281–305 (1999)

Bates, Peter W., Fife, Paul C., Ren, Xiaofeng, Wang, Xuefeng: Travelling waves in a convolution model for phase transitions. Arch. Ration. Mech. Anal. 138(2), 105–136 (1997)

Bhowmik, S.K.: Stability and convergence analysis of a one step approximation of a linear partial integro-differential equation. Numer. Methods PDEs 27(5), 1179–1200 (2011)

Bhowmik, S.K.: piecewise polynomial approximation of a nonlocal phase transitions model. Math. Anal. Appl. 420(2), 1069–1094 (2014)

Bhowmik, Samir K.: Numerical approximation of a nonlinear partial integro-differential equation. PhD thesis, Heriot-Watt University, Edinburgh, UK, April, (2008), https://sites.google.com/site/bhowmiksk/thesis

Bhowmik, Samir Kumar: Stable numerical schemes for a partly convolutional partial integro-differential equation. Appl. Math. Comput. 217(8), 4217–4226 (2010)

Bhowmik, Samir Kumar: Numerical approximation of a convolution model of $${\dot{\theta }}$$-neuron networks. Appl. Numer. Math. 61, 581–592 (2011)

Coombes, S., Lord, G.J., Owen, M.R.: Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. SIAM J. 178, 219–241 (2002)

Emmrich, Etienne, Weckner, Olaf: Anslysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity. Math. Mech. Solids 12(4), 363–384 (2007)

Batyrev, Iskander G., Becker, Richard C., Izvekov, Sergei, Patel, Parimal, Rice, Betsy M., Schuster, Brian E., Weingarten, N. Scott, Gazonas, George A., McCauley, JamesW., Wildman, Raymond A.: Multiscale modeling of non-crystalline ceramics (glass) (FY11).ARL-MR-0802 (2012)

Jackiewicz, Z., Rahman, M., Welfert, B.D.: Numerical solution of a Fredholm integro-differential equation modelling $${\dot{\theta }}-$$ neural networks. Appl. Math. Comput. 195, 523–536 (2008)

Karakoc, Seydi Battal Gazi, Bhowmik, Samir Kumar: Galerkin finite element solution for Benjamin–Bona– Mahony–Burgers equation with cubic B-splines. Comput. Math. Appl. 77(7), 1917–1932 (2019)

Laing, Carlo R., Troy, William C., Gutkin, B., Ermentrout, G.B.: Multiple bumps in a neuronal model of working memory. SIAM J. Appl. Math. 63, 62–97 (2003)

Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000)

Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations. Wadsworth and Brooks, Cole Advanced Books and Software, Pacific Grove, California (1989)

Walker, James S.: Fast Fourier Transforms. Second edition, CRC press, Boca Raton, New York, London, Tokyo (1996)

Weckner, Olaf, Emmrich, Etienne: Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. J. Comput. Appl. Mech. 6(2), 311–319 (2005)