A nondispersive and nondissipative numerical method for first-order linear hyperbolic partial differential equations

We propose a new numerical method for a solution of first-order linear hyperbolic equations. The leap-frog scheme is converted to a nondispersive scheme by introducing an adjustable constant in a fictitious absorption term. Then the erroneous decrease in th solution is eliminated by solving two equations equivalent to the original equation. The new scheme perfectly preserves the form of a discontinuous solution.