Higher-order accurate numerical solution of unsteady Burgers’ equation

High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

“…We can see from the data that when α = 0.1 in the present scheme, the fourth-order scheme in Ref. [44] and the scheme in Ref. [42] all achieve theoretical accuracy.…”

“…At the same time, the sixth-order scheme in Ref. [44] obtains sixth-order accuracy. However, the L ∞ error calculated by the sixth-order scheme in Ref.…”

“…[42] is fourth order in space, and the schemes in Ref. [44] are fourth and sixth order, respectively. We can see from the data that when α = 0.1 in the present scheme, the fourth-order scheme in Ref.…”

Effective numerical technique applied for Burgers' equation of (1 + 1)‐, (2 + 1)‐dimensional, and coupled forms

“…Numerous numerical algorithms were exploited to numerically solve NLEEs especially Burgers' equation to achieve minimized errors with respect to analytical solutions. Finite difference and other modifications, 18–24 finite element and B‐spline finite element, 25–27 spectral least squares method, 28–30 variational iteration method, 31,32 Adomian–Pade technique, 33 homotopy analysis, 34 and automatic differentiation method 35 are examples of such numerical techniques. Moreover, miscellaneous numerical techniques have been employed either for Burgers' equation or other engineering applications such as boundary element techniques for cavitation of hydrofoils, 36,37 step cubic polynomial, 38 technique of modified diffusion coefficient for studying convection diffusion equation, 39 and differential quadrature for functionally graded nanobeams 40,41 .…”

Solving one- and two-dimensional unsteady Burgers' equation using fully implicit finite difference schemes

“…The solution of the Burgers' equation is an active area through which researchers developed many numerical algorithms; and they obtained its approximate solution. These numerical algorithms depended on numerical methods such as finite difference method (Ciment, Leventhal, & Weinberg, 1978;Iskandar & Mohsen, 1992), explicit and exact explicit finite difference methods (Kutulay, Bahadir, & Odes, 1999), fourth order finite difference method (Hassanien, Salama, & Hosham, 2005), higher-order accurate finite difference method (Zhanlav, Chuluunbaatar, & Ulziibayar, 2015), collection of numerical techniques based on finite difference (Mukundan & Awasthi, 2015;Radwan, 2005), finite elements method (Dogan, 2004;Ozis, Aksan, & Ozdes, 2003), quadratic B-splines finite element method (Aksan, 2006), spectral least-squares method (Heinrichs, 2007;Maerschalck & Gerritsma, 2005;Maerschalck & Gerritsma, 2008), variational iteration method (Abdou & Soliman, 2005;Biazar & Aminikhah, 2009), Adomian-Pade technique (Dehghan, Hamidi, & Shakourifar, 2007), homotopy analysis method (Rashidi, Domairry, & Dinarvand, 2009), differential transform method and the homotopy analysis method (Rashidi & Erfani, 2009), automatic differentiation method (Asaithambi, 2010), cubic spline quasiinterpolant scheme (Xu, Wang, Zhang, & Fang, 2011), Laplace decomposition method (Khan, 2014), Bsplines collocation method (Ali, Gardner, & Gardner, 1992), Quartic B-spline collocation method (Saka & Da g, 2007), Spectral collocation method (Khalifa, Noor, & Noor, 2011;Khater, Temsah, & Hassan, 2008), Cubic Hermite collocation method (Ganaie & Kukreja, 2014), Sinc differential quadrature method (Korkmaz & Da g, 2011a), Polynomial based differential quadrature method…”