Continuous Implicit Hybrid One-Step Methods for the Solution of Initial Value Problems of General Second-Order Ordinary Differential Equations
Abstract:
The numerical solutions of initial value problems of general second order ordinary di erential equations have been studied in this work. A new class of continuous implicit hybrid one step methods capable of solving initial value problems of general second order ordinary di erential equations has been developed using the collocation and interpolation technique on the power series approximate solution. The one step method was augmented by the introduction of o step points in order to circumvent Dahlquist zero stability barrier and upgrade the order of consistency of the methods. The new class of continuous implicit hybrid one step methods has the advantage of easy change of step length and evaluation of functions at o step points. The Block method used to implement the main method guarantees that each discrete method obtained from the simultaneous solution of the block has the same order of accuracy as the main method. Hence, the new class of one step methods gives high order of accuracy with very low error constants, gives large intervals of absolute stability, are zero stable and converge. Sample examples of linear, nonlinear and sti problems have been used to test the performance of the methods as well as to compare computed results and the associated errors with the exact solutions and errors of results obtained from existing methods, respectively, in terms of step number and order of accuracy, using written e cient computer codes.ORDER COMPLETE MATERIAL (CHAPTER 1-5)
