Numerical solution of hyperbolic equations by method of bicharacteristics

Abstract

Among the numerical procedures to solve a hyperbolic system of partial differential equation. in 3-independent variables. method of bicharacteristics occupies an important position from the point of view of the accuracy of the solution. All bicharacteristic method developed so far employed the compatibility relations along, at the most, four bicharacteristics. We have presented in this paper a procedure for linear problems, taking as many bicharacteristics as possible and also have derived Butler's method as its particular case. Furthermore, stability criteria for these methods have been discussed. The present method is consistent and has second order accuracy at every time cycle and allows a timestep which is larger than that of Butler's method. A boundary method consistent with the present method has been derived. The present method has been illustrated by solving an initial-boundary value problem and a purely initial value problem, numerically and the results are compared with those of Butler's and Strang's schemes. Although Strang's scheme allows time step larger than those of bicharacteristic schemes, the bicharacteristic schemes are more accurate than Strang's scheme.