A Class of Collocation Hybrid Backward Differentiation Method for Initial Value Problems of Ordinary Differential Equations

The development of a linear multistep method for initial value problems of Ordinary Differential Equations (O.D.E.s) has been the subject of investigation for some time. In this work, a class of hybrid backward differentiation methods with step number k=1 for initial value problems of first-order ordinary differential equations was presented. The method entails interpolation of approximate solutions and collocation of the differential system. The scheme has been tested and found to be consistent and zero-stable. Numerical examples are given to demonstrate the efficiency of the new method. Keywords: Differential equations; collocation hybrid backward differential equation; initial value problems