Compact finite difference schemes with high resolution characteristics and their applications to solve Burgers equation

In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order derivatives. The proposed compact schemes have eighth order of accuracy and are tri-diagonal in nature, making use of a stencil smaller than those of conventional tri-diagonal compact finite difference schemes of the same order. They also possess high resolution properties and more resolving efficiency than conventional schemes. Some numerical experiments have been carried out, showing the good performance of the proposed schemes. Furthermore, the proposed schemes have been applied to solve with great efficiency the well-known Burgers equation.