IOP Conference Series Materials Science and Engineering · 2020 · 25 citations · 0 references
Numerical AnalysisMethod Of Fundamental SolutionNumerical ComputationEngineeringNumerical SolutionMechanicsOscillatory ProcessMechanical EngineeringNonlinear EquationComputational MechanicsQuadrature FormulasNumerical TreatmentWeakly Singular FeaturesNonlinear Mechanical SystemNumerical Method For Partial Differential Equation
Abstract The paper is devoted to the development of a numerical algorithm for solving nonlinear integro-differential equations based on the use of quadrature formulas. The Koltunov-Rzhanitsyn kernel with weakly singular features of the Abel type is used as a kernel. To conduct a computational experiment, a computer program was developed; the results obtained by this program are reflected in the form of tables and graphs. A test example was solved, and the obtained approximate numerical results were compared with exact solutions. The influence of nonlinearity and integral parts on the nature of oscillatory process of a viscoelastic body was investigated.