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

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

B-spline quasi-interpolation based numerical methods for some Sobolev type equations

In this article, we intend to use quadratic and cubic B-spline quasi-interpolants to develop higher order numerical methods for some Sobolev type equations in one space dimension. Our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence. We also discuss another approach to the cubic B-spline quasi-interpolation based method, where we achieve fourth order of accuracy in space. We theoretically establish the order of accuracy for the three proposed methods and also establish the L-2-stability in the linear case using von Neumann analysis. As a particular case of the Sobolev type equations, we take the equal width and the Benjamin-Bona-Mahony-Burgers equations, and perform several numerical experiments to support our theoretical results. (C) 2015 Elsevier B.V. All rights reserved