Comparison of high-order methods of the spatial derivative approximation in solving hyperbolic equations

The paper discusses high-order schemes for the partial spatial derivative approximation in solving hyperbolic equations. An algorithm for a recently developed finite-difference multiresolution MRWENO scheme is presented. Specific parameters are given for a fifth-order scheme. It is noted that the new scheme has interesting properties, such as the simplicity of constructing linear weights compared to the classical WENO scheme. Reconstruction in the MRWENO method is based on symmetric nested stencils. Theoretically, the method can be easily extended to any required order of accuracy. The results of the numerical solution of differential equations by various methods are presented. The solutions are compared with the analytical one and with each other. The classical WENO scheme, as the most verified, shows the best results. The MRWENO scheme combines the properties of WENO schemes with the properties of central-difference methods. The efficiency of the MRWENO method is obvious. Further calculations and theoretical research can reveal unique (different from others) properties in the method.