An Implicit Runge-Kutta Type Method for the Solution of Initial Value Problems

Abstract

In this research paper, an implicit block hybrid Backward Differentiation Formula (BDF) for 𝑘=2 is reformulated into a Runge-Kutta Type Method (RKTM) of the same step number. The method can be used to solve both first and second order (special or general form) initial value problem in Ordinary Differential Equation (ODE). This method differs from conventional BDF as derivation is done only once. It can also be extended to solve higher order ODE.