Pseudo-characteristic method of lines solution of first-order hyperbolic equation systems

First-order hyperbolic partial differential equations are difficult to solve numerically because of their ability to transmit steep waves. It is well known that the method of characteristics is the natural method for such equations, as it precisely follows wave interactions. However, a characteristic solution is expensive, as it requires repeated solution of non-linear algebraic equations. This gives considerable motivation to the development of fixed grid numerical schemes.