@Article{Arora2017, author="G. Arora, V. Joshi ", title="A computational approach using modified trigonometric cubic B-spline for numerical solution of Burgers’ equation in one and two dimensions ", journal="Alex. Eng. J.", year="2017", pages="1087–1098. ", volume="57" } @Article{Arora2013, author="G. Arora, B. K. Singh", title="Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method", journal="Appl. Math. Comput.", year="2013", pages="166–177.", volume="224" } @Article{Ashpazzadeh2017, author="E. Ashpazzadeh, B. Han, M. Lakestani", title="Biorthogonal multiwavelets on the interval for numerical solutions of Burgers’ equation", journal="J. Comput. Appl. Math.", year="2017", pages="510–534. ", volume="317" } @Article{Bahadir1999, author="A. R. Bahadir", title="Numerical solution for one-dimensional Burgers’ equation using a fully implicit finite-difference method", journal=" Int. J. Appl. Math.", year="1999", pages=" 897–909.", volume="1" } @Article{Bahadir2005, author="A. R. Bahadir, M. Saglam ", title="A mixed finite difference and boundary element approach to one-dimensional Burgers’ equation", journal=" Appl. Math. Comput.", year="2005", pages="663–673.", volume="160" } @Article{Bassi1997, author="F. Bassi, S. Rebay", title="A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations", journal=" J. Comput. Phys.", year="1997", pages="267–279.", volume="131" } @Article{Caldwell1981, author="J. Caldwell, P. Wanless, A. E. Cook", title=" A finite element approach to Burgers’ equation", journal="Appl. Math. Modelling", year="1981", pages="189–193. ", volume="5" } @Article{Chen2011, author="S. Q. Chen, Y.-T. Zhang", title=" Krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes: Application to discontinuous Galerkin methods", journal=" J. Comput. Phys.", year="2011", pages="4336–4352.", volume="230" } @Article{Cheng2017, author="Y. Cheng, X. Meng, Q. Zhang", title=" Application of generalized Gauss?Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations", journal="Math. Comp.", year="2017", pages=" 1233–1267. ", volume="86" } @Article{Cheng2017, author="Y. Cheng, Q. Zhang", title="Local Analysis of the Local Discontinuous Galerkin Method with Generalized Alternating Numerical Flux for One-Dimensional Singularly Perturbed Problem ", journal="J. Sci. Comput.", year="2017", pages="792–819.", volume="72" } @Article{Cockburn1998, author="B. Cockburn, C.-W. Shu", title="The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems", journal="SIAM J. Numer. Anal.", year="1998", pages="2440–2463. ", volume="35" } @Article{Cole1951, author="J. D. Cole", title="On a quasi-linear parabolic equation occurring in aerodynamics ", journal="Quart. Appl. Math.", year="1951", pages="225–236.", volume="9" } @Article{Gao2013, author="Y. Gao, L.-H. Le, B.-C. Shi", title="Numerical solution of Burgers’ equation by lattice Boltzmann method", journal="Appl. Math. Comput.", year="2013", pages="7685–7692. ", volume="219" } @Article{Hopf 1950, author="E. Hopf ", title="The partial differential equation \(u_t + u_x = vu_{xx}\)", journal="Comm. Pure Appl. Math.", year="1950", pages="201–230.", volume="3" } @Article{Huang2010, author="P. Huang, A. Abduwali ", title="The Modified Local Crank-Nicolson method for one-and two-dimensional Burgers’ equations ", journal="Comput. Math. Appl.", year="2010", pages="2452–2463. ", volume="59" } @Article{Jiwari 2015, author="R. Jiwari ", title="A hybrid numerical scheme for the numerical solution of the Burgers’ equation", journal=" Comput. Phys. Commun.", year="2015", pages=" 59–67.", volume="188" } @Article{Jiwari2013, author="R. Jiwari, R. C. Mittal, K. K. Sharma", title="A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers’ equation", journal=" Appl. Math. Comput.", year="2013", pages="6680–6691. ", volume="219" } @Article{Khater2008, author="A. H. Khater, R. S. Temsah, M. M. Hassan", title=" A Chebyshev spectral collocation method for solving Burgers’-type equations", journal=" J. Comput. Appl. Math.", year="2008", pages=" 333–350.", volume="222" } @Article{Kutluay1999, author="S. Kutluay, A. R. Bahadir, A. Özdeş ", title="Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference methods", journal="J. Comput. Appl. Math.", year="1999", pages="251–262.", volume="103" } @Article{Meng2016, author="X. Meng, C.-W. Shu, B. Wu ", title="Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations", journal="Math. Comp.", year="2016", pages="1225–1261.", volume="85" } @Article{Mukundan2017, author="V. Mukundan, A. Awasthi ", title="A Higher Order Numerical Implicit Method for Non-Linear Burgers’ Equation", journal="Differ. Equ. Dyn. Syst.", year="2017", pages="169–186.", volume="25" } @Article{Özdeş2003, author="T. Özdeş, E. N. Aksan, A. Özdeş", title=" A finite element approach for solution of Burgers’ equation", journal="Appl. Math. Comput.", year="2003", pages="417–428.", volume="139" } @Article{Seydaoğlu2016, author="M. Seydaoğlu, U. Erdoğan, T. Öziş", title="Numerical solution of Burgers’ equation with high order splitting methods", journal=" J. Comput. Appl. Math.", year="2016", pages=" 410–421. ", volume="291" } @Article{Shao2011, author="L. Shao, X. L. Feng, Y. N. He", title="The local discontinuous Galerkin finite element method for Burger’s equation", journal="Math. Comput. Modelling", year="2011", pages=" 2943–2954.", volume="54" } @Article{Tamsir2016, author="M. Tamsir, V. K. Srivastava, R. Jiwari", title=" An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation", journal="Appl. Math. Comput.", year="2016", pages="111–124. ", volume="290" } @Article{Xie2016, author="H. T. Xie, J. W. Zhou, Z. Jiang, X. Y. Guo", title="Approximations for Burgers equations with C-N scheme and RBF collocation methods", journal=" J. Nonlinear Sci. Appl.", year="2016", pages=" 3727–3734.", volume="9" } @Article{Zhang2012, author="R. P. Zhang, X. J. Yu, G. Z. Zhao", title="The local discontinuous Galerkin method for Burger’s-Huxley and Burger’s-Fisher equations", journal="Appl. Math. Comput.", year="2012", pages=" 8773–8778. ", volume="218" } @Article{Zhang2013, author="R. P. Zhang, X. J. Yu, G. Z. Zhao", title=" Modified Burgers’ equation by the local discontinuous Galerkin method", journal="Chinese Phys. B", year="2013", pages="106–110.", volume="22" }