Numerical solution of partial differential equations
Numerical solution of partial differential equations
A linearly implicit time integration scheme for the Burgers' equation
Neural, Parallel & Scientific Computations
Linearized box schemes for first-order systems of hyperbolic conservation laws
Neural, Parallel & Scientific Computations
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A widely used scheme in many applications for the integration of first-order systems of hyper bolic conservation laws: ut + (f(u))x =0 is the Wendroff implicit scheme, popularly known as a "box" scheme. Wendroff's scheme is based on the classical trapezoidal formula and it is a second order scheme in both time and space. In the present paper we present a high-accuracy box scheme based on the modified Simpson rule of (Chawla et al, 1994). The presented scheme is unconditionally stable and fourth order in both time and space. We include numerical experiments with the obtained scheme by considering inviscid Burgers' equation. While the solution computed by the Wendroff implicit scheme can go into oscillations near a shock, our presented scheme provides a steady approximation for the solution profile.