4-STEP EXPONENTIAL-FITTED METHODS FOR NONLINEAR PHYSICAL PROBLEMS

We describe a four-step exponential-fitted method for systems of secon d-order differential equations of the form y '' = f(x,y). This is a si xth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant f eatures are as follows: (i) it requires only two solution values to st art; (ii) it allows modification of the stepsize during the integratio n process; (iii) it works in the predictor-corrector mode with only on e function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation er ror. Our method was tested on a representative set of problems taken f rom physics and found to behave particularly well on the problems invo lving oscillatory phenomena. A selection of experimental results is gi ven in which our method is compared with a widely used code.