Numerical solutions of Troesch and Duffing equations by Taylor wavelets

Abstract

The aim of this study is obtain accurate numerical results for the Troesch and Duffing equations by using Taylor wavelets. Orthonormality property of these polynomials is an advantage of the method since it reduces the computational cost. These equations are known to be stiff equations, thus most of the numerical methods approximates the nonlinear terms and the force function while wavelets do not require such an approximation which is another advantage of the method. Troesch and Duffing equations are solved for several parameters to show the accuracy and efficiency of the applied method. Results show that the proposed method is highly efficient in the solution of indicated type of problems by using quite low degree polynomials.

Application of He’s Frequency Formula to Nonlinear Oscillators With Generalized Initial Conditions

“…where A, B and ε are constants. There is much literature to study the above problem in case of small ε or A=0/B=0 by various methods, for examples, the homotopy perturbation method [23], the energy conservation principle [24] and the variational iteration method [25].…”