Abstract
A High accurate implicit scheme based on IDO scheme for solving a wide variety of partial differential equations has been developed. By using implcit Runge-Kutta time integration, we can construct the implicit scheme with high accuracy and stability for a multi-dimensional case. It is shown that the numerical solutions for the two-dimensional advection equation and diffusion equation are equal to that of the explicit scheme for a large time interval. As examples of non-linear problems, we solved one and two-dimensional burgers equations and obtained high accurate result for a large CFL number.
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