Abstract:

The iterated variational method is considered in the approximation of eigenvalues and eigenfunctions for a class of two point boundary value problems. The implementation of this method is easy and competes well with other methods. Numerical examples are presented to show the efficiency of the method proposed. Comparison with the work of others is also illustrated.

Paper's Title:

An Easy and Efficient Way for Solving A class of Singular Two Point Boundary Value Problems

Author(s):

Muhammed I. Syam, Muhammed N. Anwar and Basem S. Attili

Mathematical Sciences Department
United Arab Emirates University, P. O. Box 17551
Al-Ain, United Arab Emirates
b.attili@uaeu.ac.ae

Abstract:

We will consider an efficient and easy way for solving a certain class of singular two point boundary value problems. We will employ the least squares method which proved to be efficient for this type of problems. Enough examples that were considered by others will be solved with comparison with the results presented there.

Paper's Title:

Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method

Author(s):

Asem AL Nemrat and Zarita Zainuddin

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
E-mail: alnemrata@yahoo.com
zarita@usm.my

Abstract:

This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the round-off errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).

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