| Summary: | The paper considers direct methods for integrating nonlinear equations of dynamics. Two approaches have been identified for approximating the equations during a small provisional segment. In the first, a more approximate approach is considered, in which the displacements are approximated only with the cross rigidity of the system at the current moment. In the second, an approach in displacement increments is considered, when the change in the system response is differentiated by the achieved level of displacements and their increments at the time step. Different schemes of forth integration for the nonlinear equations in the first and second approaches are considered. The absolute stability of the new proposed schemes of forth integration is proved when using a more accurate approximation in displacements. Theoretical results are supported by the model examples solution for which the exact solution, or the solution in the series is known.
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