Moses Adebowale Akanbi

On 3-stage geometric explicit Runge–Kutta method for singular autonomous initial value problems in ordinary differential equations

There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving autonomous initial value problems in ordinary differential equations is derived and implemented. The computational results show that the method is stable, efficient and accurate. We also compared this method with some other conventional methods.

Application of Geometric Explicit Runge–Kutta Methods to Pharmacokinetic Models

In an earlier work, the authors proposed a class of geometric explicit Runge– Kutta methods for solving one-dimensional first order Initial Value Problems (IVPs). In this work, some members of this class of schemes which were found to be more accurate are applied to systems of first order ordinary differential equations (ODEs). We present the development of these selected schemes and also study their basic properties vis-a-vis systems of ODEs. We then apply this approach to solve some mathematical models arising in Pharmacokinetics.

Step Size Bounds for a Class of Multiderivative Explicit Runge–Kutta Methods

A class of 3-Stage Multiderivative Explicit Runge-Kutta Methods was developed for the solution of Initial Value Problems (IVPs) in Ordinary Differential Equations. In this work, we present the bounds on the step size required for the implementation of this family of methods. This bound is one of the parameter required in the design of program codes for solving IVPs. A comparison of the step size bound was made vis-a-vis the existing Explicit Runge-Kutta Methods using some standard problems. The computation shows that the family of methods competes well with the popular methods.