This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then t...

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in article Caputo–Fabrizio and Atangana–Baleanu derivative. We employed transform on followed by inverse transform, to achieve result equations. To validate method, considered a examples compared exact ...

Abstract In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two scenarios examined each operator: when initial conditions u(x, y, 0) = sin(xy), v(x, they e {−kxy} , where k, α some positive constants. With aid computable ...