The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Ali Tavakoli - One of the best experts on this subject based on the ideXlab platform.
-
Interpolated variational iteration method for Initial Value Problems
Applied Mathematical Modelling, 2016Co-Authors: Davod Khojasteh Salkuyeh, Ali TavakoliAbstract: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 the sequence become complicated, and therefore, computing a highly accurate solution would be difficult or even impossible. In this paper, for one-dimensional Initial Value Problems, we propose a new approach which is based on approximating each term of the sequence by a piecewise linear function. Moreover, the convergence of the method is proved. Three illustrative examples are given to show the superiority of the proposed method over the classical variational iteration method.Comment: 17 pages, 8 figures in Applied Mathematical Modelling, 201
-
Interpolated variational iteration method for Initial Value Problems
Applied Mathematical Modelling, 2015Co-Authors: Davod Khojasteh Salkuyeh, Ali TavakoliAbstract:Abstract In order to solve an Initial Value problem by the variational iteration method, a sequence of functions is produced that converges to the solution under suitable conditions. In the nonlinear case, the terms of the sequence become complicated after a few iterations, and thus computing a highly accurate solution is difficult or even impossible. In this study, we propose a new approach for one-dimensional Initial Value Problems, which is based on approximating each term of the sequence by a piecewise linear function. Moreover, we prove the convergence of the method. Three illustrative examples are given to demonstrate the superior performance of the proposed method compared with the classical variational iteration method.
P Mutalik B Desai - One of the best experts on this subject based on the ideXlab platform.
-
haar wavelet collocation method for the numerical solution of singular Initial Value Problems
Ain Shams Engineering Journal, 2016Co-Authors: S C Shiralashetti, A B Deshi, P Mutalik B DesaiAbstract:Abstract In this paper, numerical solutions of singular Initial Value Problems are obtained by the Haar wavelet collocation method (HWCM). The HWCM is a numerical method for solving integral equations, ordinary and partial differential equations. To show the efficiency of the HWCM, some examples are presented. This method provides a fast convergent series of easily computable components. The errors of HWCM are also computed. Through this analysis, the solution is found on the coarse grid points and then converging toward higher accuracy by increasing the level of the Haar wavelet. Comparisons with exact and existing numerical methods (adomian decomposition method (ADM) & variational iteration method (VIM)) solutions show that the HWCM is a powerful numerical method for the solution of the linear and non-linear singular Initial Value Problems. The Haar wavelet adaptive grid method (HWAGM) based solutions show the excellent performance for the proposed Problems.
Nickolai Kosmatov - One of the best experts on this subject based on the ideXlab platform.
-
Initial Value Problems of fractional order with fractional impulsive conditions
Results in Mathematics, 2013Co-Authors: Nickolai KosmatovAbstract:In this paper we intend to accomplish two tasks firstly, we address some basic errors in several recent results involving impulsive fractional equations with the Caputo derivative, and, secondly, we study Initial Value Problems for nonlinear differential equations with the Riemann–Liouville derivative of order 0 < α ≤ 1 and the Caputo derivatives of order 1 < δ < 2. In both cases, the corresponding fractional derivative of lower order is involved in the formulation of impulsive conditions.
-
integral equations and Initial Value Problems for nonlinear differential equations of fractional order
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Nickolai KosmatovAbstract:Abstract We discuss the solvability of integral equations associated with Initial Value Problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray–Schauder Nonlinear Alternative for several types of Initial Value Problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the “reduction” of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator.
Davod Khojasteh Salkuyeh - One of the best experts on this subject based on the ideXlab platform.
-
Interpolated variational iteration method for Initial Value Problems
Applied Mathematical Modelling, 2015Co-Authors: Davod Khojasteh Salkuyeh, Ali TavakoliAbstract:Abstract In order to solve an Initial Value problem by the variational iteration method, a sequence of functions is produced that converges to the solution under suitable conditions. In the nonlinear case, the terms of the sequence become complicated after a few iterations, and thus computing a highly accurate solution is difficult or even impossible. In this study, we propose a new approach for one-dimensional Initial Value Problems, which is based on approximating each term of the sequence by a piecewise linear function. Moreover, we prove the convergence of the method. Three illustrative examples are given to demonstrate the superior performance of the proposed method compared with the classical variational iteration method.
-
Two-stage waveform relaxation method for the Initial Value Problems with non-constant coefficients
Computational & Applied Mathematics, 2013Co-Authors: Zeinab Hassanzadeh, Davod Khojasteh SalkuyehAbstract:In this paper, we present a two-stage waveform relaxation method applied to the Initial Value Problems for the linear systems of ordinary differential equations in the form \(y'(t)+A(t)y(t)=f(t)\). By making use of the forward Euler method, we derive sufficient conditions for the convergence of this method, when \(A(t)\) is M-matrix for every \(t\in [t_0, T]\). Finally some numerical experiments are given to illustrate some of the theoretical results.
S C Shiralashetti - One of the best experts on this subject based on the ideXlab platform.
-
haar wavelet collocation method for the numerical solution of singular Initial Value Problems
Ain Shams Engineering Journal, 2016Co-Authors: S C Shiralashetti, A B Deshi, P Mutalik B DesaiAbstract:Abstract In this paper, numerical solutions of singular Initial Value Problems are obtained by the Haar wavelet collocation method (HWCM). The HWCM is a numerical method for solving integral equations, ordinary and partial differential equations. To show the efficiency of the HWCM, some examples are presented. This method provides a fast convergent series of easily computable components. The errors of HWCM are also computed. Through this analysis, the solution is found on the coarse grid points and then converging toward higher accuracy by increasing the level of the Haar wavelet. Comparisons with exact and existing numerical methods (adomian decomposition method (ADM) & variational iteration method (VIM)) solutions show that the HWCM is a powerful numerical method for the solution of the linear and non-linear singular Initial Value Problems. The Haar wavelet adaptive grid method (HWAGM) based solutions show the excellent performance for the proposed Problems.
