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In recent years, Boris, Book and Hain have proposed a family of finite difference methods called FCT techniques for the Cauchy problem of the continuity equation. The purpose of this paper is to study the stability and convergence about the SHASTA FCT algorithm, which is one of the basic schemes among many FCT techniques, though not in its original form but a slightly modified one for our technical reason. (Our numerical experiments indicate less distinction between the algorithm dealt with here and the original SHASTA FCT one in terms of reproduction ofsharp discontinuities.) The main results are Theorems 1 and 2 concerning the L -stability and the Ljoc-convergence, respectively.

On the SHASTA FCT algorithm for the equation ∂𝜌/∂𝑡+(∂/∂𝑥)(𝑣(𝜌)𝜌)=0