MATH-PHAug 16, 2010
Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domainsK. Parand, A. R. Rezaei, A. Taghavi
In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is acceptable.
MATH-PHAug 16, 2010
Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparisonK. Parand, A. R. Rezaei, A. Taghavi
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.