Abstract
Two families of two-time level difference schemes are developed for the numerical solution of first-order hyperbolic partial differential equations with one space variable. The space derivative is replaced by (i) a first-order, (ii) a second-order backward difference approximant, and the resulting system of first-order ordinary differential equations is solved using A 0-stable and L 0-stable methods. The methods are used explicitly and are inexpensive to implement. The methods are tested on a number of problems from the literature involving wave-form solutions, increasing solutions with discontinuities in function values or first derivatives across a characteristic, and exponentially decaying solutions.
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