Impact of human activities on physicochemical parameters and nutrient distribution in the surface water of Ayetoro community, Ilaje, South West Nigeria

In this paper, a new iterative method to solve linear and nonlinear initial boundary value problem (IBVP) with non local conditions was developed. The new method is an elegant combination of traditional variational iteration and the decomposition methods.  Several examples are presented to verify the accuracy and efficiency of this new method with the exact solution. This new iterative method developed may be suitable for teaching andbetter understanding of some advanced undergraduate courses on analytical and classical mechanics

Application of new iterative method for solving linear and nonlinear initial boundary value problems with non local conditions

In this paper, a new iterative method to solve linear and nonlinear initial boundary value problem (IBVP) with non local conditions was developed. The new method is an elegant combination of traditional variational iteration and the decomposition methods.  Several examples are presented to verify the accuracy and efficiency of this new method with the exact solution. This new iterative method developed may be suitable for teaching andbetter understanding of some advanced undergraduate courses on analytical and classical mechanics

Algorithm for solving a generalized Hirota-Satsuma Coupled KdV equation using homotopy perturbation transform method

In this paper, we merge homotopy perturbation method with He’s polynomials and Laplace transformation method to produce a highly effective algorithm for finding approximate solutions for generalized Hirota-Satsuma Coupled KdV equations. This technique is called the Homotopy Perturbation Transform Method (HPTM). With this technique, the solutions are obtained without any discretization or restrictive assumptions, and devoid of roundoff errors. This technique solved a generalized Hirota-Satsuma Coupled KdV equation without using Adomian’s polynomials which can be considered as a clear advantage over the decomposition method. MAPLE software was used to calculate the series generated from the algorithm. The results reveal that the homotopy perturbation transform method (HPTM) is very efficient, simple and can be applied to other nonlinear problems.Keywords: Coupled KdV equations, Homotopy perturbation transform method, Laplace transform method, Maple software, He’s polynomia