SIAM Journal on Numerical Analysis, Vol. 31, No. 3 (Jun., 1994), pp. 655-679 (25 pages) The accuracy of numerical approximations to piecewise smooth solutions of hyperbolic partial differential ...
Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...
Convergence results for bounded time intervals are well known for finite difference approximations to the Cauchy problem for hyperbolic equations. These results typically state that if the initial ...
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