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In this paper novel techniques for nonlinear frequency domain region problems with respect to linearity are examined. A notable methodology called as Modified Euler’s method and improved Euler’s method to perform nonlinear recurrence domain investigations of RLC circuit problems. Here a combination of waves approximates the driving forces to attain its damped oscillatory solutions. The two different cases were analyzed as, stability of the RLC circuit when the applied voltage is equal to zero and the forced oscillations of the RLC circuit when the applied voltage is equal to ?0?????. To keen the strength of investigation, stability analysis and non-oscillatory behavior of the RLC circuit are explained along with periodical time.