Sensitivity of the numerical analysis of the three-fluid plasma mixed initial-boundary value problem

Abstract

The sensitivity of the numerical solution of the nonlinear three-fluid equations governing the effect of forcing a time dependent disturbance at a point in a plasma is investigated. With the equations transformed into a diagonal form it is shown that only certain variables may be prescribed as functions of time at x=0, where these specified functions must satisfy certain compatibity conditions. With forward differences used to replace the time derivative and either forward or backward differences used to replace the spatial derivatives, the difference equations formulated are consistent and their solution converges to the solution of the differential equations. This convergence is true as long as the domain of dependence concept is adhered to. A lineary analysis provides a guide to the actual stability of the system of equations. From this analysis it is seen that the magnitude of the collission frequences, as well as the speed of light, restricts the size of the steps which may be used. Furthermore, it is shown that the solution is extremely sensitive to the boundary and initial conditions specified. © 1973.