Optimized basis expansion as an extremely accurate technique for solving   time-independent Schr\"odinger equation
  We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic oscillator perturbed by a trigonometric anharmonic term as not exactly solvable cases and obtain the nearly exact solutions. 
P. Pedram, M. Mirzaei, and S.S. Gousheh