New higher order Haar wavelet method: Application to FGM structures

A new higher order Haar wavelet method (HOHWM) has been developed for solving differential and integro-differential equations. Generalized approach has been proposed for wavelet expansion allowing improvement of the accuracy and the rate of convergence of the solution. The sample problem considered shows, that applying the approach proposed allows to improve the order of convergence of the HWM from two to four and to reduce the absolute error by several orders of magnitude (depending on mesh). Furthermore, in the case of sample problem considered, the computational and implementation complexities are kept in the same range with widely used HWM.