Derivation of a New One-Step Numerical Integrator for Solving First Order Ordinary Differential Equations

This article presents a new class of one-step second derivative hybrid block method to solve general first order initial value problems of ordinary differential equations. The method is derived by interpolating an approximated power series at one point and collocating its first and second derivatives at some carefully selected intra-step points. The method is implemented in a block form to overcome the setbacks of applying starting values and predictors. The basic properties of the method were analysed and found to be a method of order of accuracy 10 and A-stable. The efficacy of the method is tested on several first order ordinary differential equations which include autonomous and non-autonomous equations, stiff systems and oscillatory problems and results compared with exact solutions.