Numerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation method

In this study, we analyze the performance of a numerical scheme based on 3-scale Haar wavelets for dynamic Euler-Bernoulli equation, which is fourth order time dependent partial differential equation. This type equations governs behaviour vibrating beam and have many applications in elasticity. For its solution, first rewrite equation as system by introducing new variable, then use finite difference approximations to discretize time, well space. By doing so, obtain algebraic whose solution gives wavelet coefficients constructing To test accuracy reliability wavelets, apply it five problems including variable constant coefficient, homogeneous non-homogeneous equations. The obtained results are compared wherever possible with those from previous studies. Numerical tabulated depicted graphically. proposed method, achieve high even small number collocation points.