Piecewise parabolic method on local stencil. I. Advection equation and Burgers' equation

Modification of piecewise parabolic method reducing dissipation of it due to exclusion the interpolation procedure on four-point stencil suggested. Comparison with standard piecewise parabolic method (PPM) was carried out with the help of test problems for linear advection equation and for inviscid Burgers' equation. The comparison was carried out on the basis of values of errors in different norms.