Related papers: On the numerical Picard iterations method with col…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…
The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We give explicit formulas as well as a quadratic time algorithm to solve (so called) generalized Vandermonde's systems of p linear equations and n variables. It allows in particular to find all (so called Lagrange's) interpolation polynoms…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…
In this work we show how auxiliary variables can be used to give an efficient method involving symbolic manipulation and Picard iteration for approximating solutions of certain Volterra integral equations.
In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
In this work we give an efficient method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of two-point boundary value problems.
In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…