Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics

Abstract

The paper is concerned with two possible numerical variations based on the use of characteristics, and the results obtained provide a basis for comparison with an analogue method described in another paper. The more common approach of differencing along both sets of characteristics and solving at the characteristic-grid points is compared with the alternative approach of numerically solving the ordinary differential equations arising from the analogue approach. Digital-computer solutions, based on these two alternative methods, are obtained for three typical hyperbolic equations. The results give some indication of the significant advantage to be gained by the latter method over the characteristic-grid method, while retaining the advantage of convergence of the grid method. These advantages are of special interest in approximate modelling of distributed-parameter systems involved in the application of control methods.