Approximate solution for the system of Non-linear Volterra integral equations of the second kind by using block-by-block method,”

Abstract: The aim of this paper is for finding the numerical solution (sometimes exact) for non-linear system of Volterra integral equations of the second kind (NSVIEK2) by using block-by-block method. W hich avoid the need for special starting procedures, but uses numerical quadrature rule. Also some illustrative examples are presented, to elucidate the accuracy of this method

Solving a System of Linear Fredholm Fractional Integro-differential Equations Using Homotopy Perturbation Method

Abstract: Homotopy perturbation method has been employed to obtain a solution of a system of linear Fredholm fractional integro-differential equations: where denotes Remann -Leiouville fractional derivatives

Adomian Decomposition Method for Solving System of Delay Differential Equation

Abstract: In this article we use Adomian decomposition method (ADM), to solve system of delay differential equations of the first order and delay differential equations of higher order by converting it into a system of delay differential of the first order. Some examples are presented to show the ability of the method for linear and non-linear system of delay differential equations

Natural Sciences Publishing Cor.

Iterative methods for solving nonlinear equations by using quadratic spline functio

Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations

Steffensen-type methods with memory were originally designed to solve nonlinear equations without the use of additional functional evaluations per computing step. In this paper, a variant of Steffensen’s method is proposed which is derivative-free and with memory. In fact, using an acceleration technique via interpolation polynomials of appropriate degrees, the computational efficiency index of this scheme is improved. It is discussed that the new scheme is quite fast and has a high efficiency index. Finally, numerical investigations are brought forward to uphold the theoretical discussions

Spectral Properties of Second Order Differential Equations with Spectral Parameter in the Boundary Conditions

Abstract: In this paper, we found the location and asymptotic of the eigenvalues of the linear differential equation −y ′ ′ + q(x)y=λ 2 p(x)y,x∈(0,a) with the boundary conditions y ′ (a)+iλy(a)=y ′ (0)+iλy(0)=0 when ρ(x)>0 and the normalized condition ∫ a 0 ρ(x)|y(x) | 2 dx=1, where λ is a spectral parameter