Investigation of Nondissipative Discontinuity Structures for Equations of Micropolar Magnetoelastic Medium and Development of a General Approach to the Numerical Solution of Evolutionary Partial Differential Equations

Numerical solutions to magnetoelasticity equations are considered. A numerical scheme based on central differences for spatial derivatives and the fourth-order Runge-Kutta method for time derivatives is used. The initial data is a solitary wave and a smoothed step (Riemann problem). The study is carried out beginning with simpler equations and continues for more complex ones. New types of discontinuity structures are found, and the conditions for the correctness of the equations are investigated.