The method of the joint approximation for solving the multi-dimensional quasi-linear hyperbolic equations - Бучарский, Валерий Леонидович (Eastern-European Journal of Enterprise Technologies, 2013)
In present paper the method of the joint approximation for constructing high order of accuracy finite difference schemes is extended on the case of multidimensional quasi-linear hyperbolic equations. The new two-step cost-effective way for constructing compact cost-effective finite difference schemes with unlimited order of accuracy is suggested. This approach is based on the method of the joint approximation and one property of the hyperbolic partial derivatives equations. Finite difference schemes up to seventh order of temporal and spatial accuracy for the two-dimensional linear transport equation and the two-dimensional Burgers equation are presented. Results of the solution of the used widely test cases are presented also. The data of the calculations confirm the theoretical results