A Newiterative Integrator for Cauchy Problems

Abstract

The paper proposes a new iterative integrator capable of solving first order initial value problems (IVPs), also called Cauchy problems, in ordinary differential equations (ODEs). The integrator was found to be superior to Forward Euler’s Method (FoEM) and achieves second order accuracy making it comparable to Ralston’s, explicit trapezoidal and midpoint methods. Consistency, Convergence and Stability are met. The derivation of the scheme depends on the idea of combining a constant and an exponential function. The integrator is numerically tested and compared with methods discussed in literature. Numerical computations have been carried out via MATLAB programming language.