SOME MODIFIED RUNGE-KUTTA METHODS FOR THE NUMERICAL-SOLUTION OF SOME SPECIFIC SCHRODINGER-EQUATIONS AND RELATED PROBLEMS

Some new modified Runge-Kutta methods with minimal phase lag are devel oped for the numerical solution of the eigenvalue Schrodinger equation and related problems with oscillating solutions. These methods are ba sed on the very well-known Runge-Kutta method of order 4. For the nume rical solution of the eigenvalue Schrodinger equation, we investigate two cases: (i) the specific case in which the potential V(x) is an eve n function with respect to x; it is assumed, also, that the wave funct ions tend to zero for x --> +/-infinity; (ii) the general case for the well-known cases of the Morse potential and Woods-Saxon or optical po tential. Also, we have applied the new methods to some well-known prob lems with oscillatory solutions. Numerical and theoretical results sho w that this new approach is more efficient than the well-known classic al fourth order Runge-Kutta method and the Numerov method.