A system of ordinary differential equations(ODEs)is produced by the semi-discretize method of discretizing the advection diffusion equation(ADE).Runge-Kutta methods of the second and fourth orders are used to solve th...A system of ordinary differential equations(ODEs)is produced by the semi-discretize method of discretizing the advection diffusion equation(ADE).Runge-Kutta methods of the second and fourth orders are used to solve the system of ODEs.We compute the ADE numerically for initial and boundary conditions,for which the exact solution is known.In the semi-discretization approach,we estimate the error for both the second and fourth-order Runge-Kutta schemes.The semi-discretization method’s outcome is contrasted with the ADE’s numerical solution derived from the complete discretization ex-plicit centered difference scheme.展开更多
文摘A system of ordinary differential equations(ODEs)is produced by the semi-discretize method of discretizing the advection diffusion equation(ADE).Runge-Kutta methods of the second and fourth orders are used to solve the system of ODEs.We compute the ADE numerically for initial and boundary conditions,for which the exact solution is known.In the semi-discretization approach,we estimate the error for both the second and fourth-order Runge-Kutta schemes.The semi-discretization method’s outcome is contrasted with the ADE’s numerical solution derived from the complete discretization ex-plicit centered difference scheme.
