Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

Susmita Paul,Paritosh Bhattacharya,Sankar Prasad Mondal,Kripasindhu Chaudhuri

doi:10.1155/2016/8921710

Abstract

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM) and with the exact solutions.

Highlights

IntroductionMathematical models of population growth have been formed to provide a significant angle of the real ecological situation
The numerical solutions obtained by using the RKF, Laplace Adomian Decomposition Method (LADM) method and are compared with the exact solution for different population models
We describe the method for finding numerical solution of insect population model and Lotka-Volterra model

Summary

Introduction

Mathematical models of population growth have been formed to provide a significant angle of the real ecological situation. The meaning and importance of each parameter in the models have been defined biologically [1, 2]. In case of insect population, birth and death rate of a species typically are not constant; instead, they vary periodically with the passage of seasons, whereas the Lotka-Volterra equations demonstrate an arbitrary number of ecological competitors (or predator-prey) model which is dynamic in nature. The population growth model is very important in mathematical biology which is used basically to demonstrate a simple nonlinear control system in population growth

Objectives

Results

Conclusion