A method for calculating generalized solutions to the one-dimensional linear advection equation
The author develops a numerical method for calculating generalized solutions to the transport equation in the case of one-dimensional spatial variable. He constructs a class of numerical schemes which guarantee a higher-order approximation to generalized solutions for the transport equation. The construction of these schemes is based on expansion of the generalized solutions under consideration into the sum of smooth and singular parts. The advantage of the method suggested is that the schemes make it possible to avoid loss of accuracy which is inevitable for almost all methods in practice.
scientific article; zbMATH DE number 1603344