An Operator Splitting Method for Convection-diffusion Equations
نویسندگان
چکیده
We present a semi-discrete method for constructing approximate solutions to the m-dimensional (m 1) convection-diiusion equation ut + r f(u) = "u. The method is based on the use of operator splitting to isolate the convection part and the diiusion part of the equation. In the case m > 1, dimensional splitting is used to reduce the m-dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence of approximate solutions. Finally, a fully discrete method is analyzed, and demonstrated in the case of one and two space dimensions.
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