Numerical solutions to differential equations with strong nonlinearities based on series expansion of orthogonal scaling functions
Zhou Youhe · Journal of Lanzhou University · 2010
An approach was developed to compute the multiple integrations of a function based on the series expansion of scaling functions of orthogonal wavelets.The proposed approach was then applied to solving differential equations with strong nonlinearity,where the unknown function was approximated by scaling function expansion as used in the classical wavelet-Galerkin method,but no calculations of connection coefficients were necessary during the solution procedures,thus significantly reducing the computational complexity and avoided additional numerical errors.The efficiency of the approach was demonstrated by solving a two-point boundary value problem with logarithm nonlinearity.