This paper deals with the analytical approximate solution of Abel differential equations (ADEs)

of the type du/dt = Σmk=0 gk(t)uk by proposing a new modified version of the parametric iteration

method (PIM). ...

his paper presents a new iterative method for computing the approximate inverse of non-singular matrices. The analytical discussion of the method is included to demonstrate its convergence behavior. As a matter of fact, it is proven...

In this paper, we use measure theory for solving well known shortes path problem. Our approach is not iterative, and we obtain an approximate optimal sloution in a straightforward manner.

In this paper, we use a technique for solving integral equations which

is based on He’s variational iteration method. In this approach, at first,

we turn the given integral equation to the integro-differential equation

and next...

This paper deals with a new proof of convergence of He’s variational iteration method applied to nonlinear oscillators. One example is given to verify convergence hypothesis and to illustrate the efficiency and simplicity of the method....

By using homotopy analysismethod (HAM), we introduce an iterative method for solving linear systems.This method (HAM) can be used to accelerate the convergence of the basic iterative methods. We also show that by applying HAM to a divergent...

The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals...

The piecewise variational iteration method (VIM) for solving Riccati differential equations (RDEs) provides a solution as a sequence of iterates. Therefore, its application to RDEs leads to the calculation of terms that are not needed and more time...