RATIONAL BLOCK METHOD FOR THE NUMERICAL SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS

Abstract

This project is devoted to studying 2-point explicit rational block methods which are used to compute the numerical solution of first order initial value problems. Rational block methods are preferred because they possess absolute stability property unlike existing block methods that are based on polynomial approximants. Two explicit rational block methods, namely A-stable 2- point explicit rational block method and L-stable 2-point explicit rational block method are derived and discussed in detail. The A-stable 2-point explicit rational block method is shown to have second order accuracy while the L-stable 2-point explicit rational block method has first order accuracy. The absolute stability of these two methods were analyzed and it is found that the former has left hand half plane assuring it is A-stable while the latter method has a finite region of absolute stability which means it is L-stable. To illustrate the efficiency of the proposed methods, some test problems are solved and the results are compared with two existing rational methods via the constant step size approach. The numerical results show that the proposed 2- point explicit rational block methods perform better and provide more accurate solutions.