A new class of strong stability preserving general linear methods

We systematically investigate strong stability preserving general linear methods of order p, stage order q=p or q=p−1, with r=p+1 external approximations, and s=p−1 internal approximations, for numerical solution of differential systems. Examples of methods of order p and stage order q=p or q=p−1, with large strong stability preserving coefficients and large regions of absolute stability, are provided for p=2, p=3, and p=4. The results of numerical experiments confirm that the methods constructed in this paper achieve the expected order of accuracy, do not produce spurious oscillations, and they are suitable to preserve the monotonicity of the numerical solution, when applied to discretization of hyperbolic conservation laws with discontinuous initial conditions.