Solution of the Burgers Shock Wave Equation in PTC MathCAD

Dmitrii Stepanov, Aleksandr Gukasyan, Vycheslav Kosachev, Raisa Oleynikova
2020 Procedia Computer Science  
A technique for solving the Burgers equation by the Galerkin method as applied to the problem of a propagating shock wave is considered. The solution is based on the reduction of a parabolic partial differential equation to a system of ordinary differential equations, depending on time, considering the nonlinear term included into the differential equation. The system of ordinary differential equations is integrated using the Euler computational scheme. Furthermore, the step size is maintained
more » ... mall enough so that the errors associated with numerical integration are negligible in comparison with the approximation error. It is established that the mean square error with an increase in the order of the approximate solution decreases rapidly and the trial solution converges to the exact solution. Abstract A technique for solving the Burgers equation by the Galerkin method as applied to the problem of a propagating shock wave is considered. The solution is based on the reduction of a parabolic partial differential equation to a system of ordinary differential equations, depending on time, considering the nonlinear term included into the differential equation. The system of ordinary differential equations is integrated using the Euler computational scheme. Furthermore, the step size is maintained small enough so that the errors associated with numerical integration are negligible in comparison with the approximation error. It is established that the mean square error with an increase in the order of the approximate solution decreases rapidly and the trial solution converges to the exact solution.
doi:10.1016/j.procs.2020.03.409 fatcat:hc3wgbhxg5c65ii4fenpq45oqe