Erratum to: Increasing Approximate-Solution Accuracy by Using Perturbation Theory

approximate solution to boundary value problems by the modified vim

this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.

Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

Approximate Solution of the Second Order Initial Value Problem by Using Epsilon Modified Block-Pulse Function

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their oper...

Approximate Analytical Solution of 3D Fractional Microscale Heat Equation Using Modified Homotopy Perturbation Method

In the present article, we use modified homotopy perturbation method (HPM) to find approximate analytical solution of three-dimensional time fractional microscale heat transport equation. This transport equation is at first converted into the equation of two functions. First one have both, the first order fractional time derivative and second order space derivatives, while second one has only s...

Approximate Solution of Convection- Diffusion Equation by the Homotopy Perturbation Method