A new approach for solving Duffing equations involving both integral and non-integral forcing terms

In this paper a Legendre wavelet operational matrix of derivative (LWOM) is used to solve the Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions. This operational matrix method together with Gaussian quadrature formula converts the given Duffing equation into system of algebraic equations, which indeed makes computation of solution easier. The applicability and simplicity of the proposed method is demonstrated by some examples and comparison with other recent methods. It is to be noted that, to the best of our knowledge, no wavelet based method applied for solving Duffing equations so far.