Abstract
Implicit finite difference schemes are developed for the efficient numerical integration of one- and two-dimensional scalar hyperbolic equations and a system of conservation laws, using the spline (in compression) function approximation. The difference schemes for one space dimension are of second-order accuracy, dissipative of order four and unconditionally stable. The algorithms for two space dimensions are second-order accurate and non-iterative. The difference schemes have been applied to problems with smooth and discontinuous initial conditions.
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