A comparison of three numerical techniques used for the solution of the two-point boundary value problem

Three numerical approximation techniques, called the Initial step, Shooting, and Direct Finite Difference Techniques, respectively, are compared and discussed as they apply to the solution of both linear and non-linear boundary-value problems of the form y =f(x,y,y\u27) with endpoint conditions y(xo)=yo and y(xn)=yn. The techniques are compared with respect to speed and accuracy by comparing the solution of each problem considered four times, each time for a different increment value, and comparing the errors at four pivotal points chosen at equally spaced distances over the domain of the function, to give an indication of the accuracy of each technique over the complete interval. For each technique, a detailed discussion of limitations and difficulties which affect the solution of the boundary-value problem is studied. Also modifications to increase accuracy and speed are suggested for the techniques. The results of this study show that each technique has certain advantages and disadvantages for particular types of boundary-value problems. However, when a large number of different boundary-value problems are considered, none of the techniques is always considered most appropriate --Abstract, page ii