Solving Initial Value Problems by Flower Pollination Algorithm

Abstract

Differential equations are very important in modeling many phenomena mathematically. The aim of this paper is to consider Initial Value Problems (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to find numerical approximation of (IVPs) since they can almost be solved simply by classical mathematical tools which are not very precise. By selecting a methodical way based on the use of recent and efficient algorithm, that is, Flower Pollination Algorithm (FPA), inspired by the pollination process of flowers plants to solve approximately an (IVP) when a specified example is selected that is the exponential problem which have an imperative role to describe many real problems. The effectiveness of the proposed method is tested via a simulation study between the exact results, the FPA results and Euler method which is considerate as a classical tool to solve numerically an (IVP). The final results and after a comparison between the performance of FPA and Euler method in terms of solution quality shows that FPA yields satisfactorily precise approximation of the solution. That ensures the ability of FPA to solve such important problems and highly complexes problems efficiently with minimal error.