Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions

In the present work, a new approximated method for solving nonlinear Duffing-Van der Pol (D-VdP) oscillator equation is suggested. The approximate solution of this introduced with two separate techniques. First, we convert D-VdP to Volterra integral second kind (VIESK) using integration, and then, it hybrid Legendre polynomials block-pulse function (HLBPFs). next technique into system ordinary differential first order (SODE) solve according proposed method. main goal presented transform these problems algebraic equations operational matrix obtained from which can be solved by proper numerical method; thus, procedures are either reduced or simplified accordingly. benefit functions that they adjusted different values n id="M2"> m , in addition being capable yield greater correct answers than piecewise constant orthogonal function, results equations. Resolved governance Runge-Kutta fourth algorithm stepping time 0.01 s via solution. show effective. evaluation has been proven good agreement other methods.