Variational iterative method and initial-value problems

2009 ◽  
Vol 215 (1) ◽  
pp. 276-282 ◽  
Author(s):  
Malik Mamode
Keyword(s):  
Iterative Method ◽  
Initial Value Problems ◽  
Initial Value ◽  
Variational Iterative Method

scholarly journals An Iterative Method for Time-Fractional Swift-Hohenberg Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjin Li ◽  
Yanni Pang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Cauchy Problems ◽  
Initial Value ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

We study a type of iterative method and apply it to time-fractional Swift-Hohenberg equation with initial value. Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations.

Solution of fractional partial differential equations using iterative method

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Chandradeepa Dhaigude ◽  
Vasant Nikam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
Fractional Partial Differential Equations ◽  
Initial Value ◽  
Diffusion Wave ◽  
Linear And Nonlinear

AbstractThe purpose of this paper is to obtain solutions for both linear and nonlinear initial value problems (IVPs) for fractional transport equations and fractional diffusion-wave equations using the iterative method.

scholarly journals On Effects of a New Method for Fractional Initial Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hülya Kodal Sevindir ◽  
Süleyman Çetinkaya ◽  
Ali Demir
Keyword(s):  
Iterative Method ◽  
Fractional Derivative ◽  
Infinite Series ◽  
Initial Value Problems ◽  
Analytic Solution ◽  
Initial Value ◽  
Transform Method ◽  
Series Form ◽  
Time Fractional Derivative ◽  
A New Technique

The aim of this study is to analyze nonlinear Liouville-Caputo time-fractional problems by a new technique which is a combination of the iterative and ARA transform methods and is denoted by IAM. First, the ARA transform method and its inverse are utilized to get rid of time fractional derivative. Later, the iterative method is applied to establish the solution of the problem in infinite series form. The main advantages of this method are that it converges to analytic solution of the problem rapidly and implementation of method is easy. Finally, outcomes of the illustrative examples prove the efficiency and accuracy of the method.

scholarly journals Modified New Iterative Method for Solving Nonlinear Partial Differential Equations

2020 ◽  
Vol 19 ◽  
pp. 1-10
Author(s):  
Alaa K. Jabber
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Linear Differential Operator ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
The Laplace Transform ◽  
Linear Differential ◽  
New Iterative Method

In this paper, the iterative method, proposed by Gejji and Jafari in 2006, has been modified for solving nonlinear initial value problems. The Laplace transform was used in this modification to eliminate the linear differential operator in the differential equation. The convergence of the solution was discussed according to the modification proposed. To illustrate this modification some examples were presented.

scholarly journals Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-30 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Shafiq Ur Rehman ◽  
Malik Zaka Ullah ◽  
Hani Moaiteq Aljahdali ◽  
Shahid Ahmad ◽  
...  
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
Lu Factorization ◽  
Single Application ◽  
Initial Value ◽  
Comprehensive Comparison

In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. Frozen Jacobian multistep iterative methods are computationally very efficient. They require only one inversion of the Jacobian in the form of LU-factorization. The LU factors can then be used repeatedly in the multistep part to solve other linear systems. The convergence order of the proposed iterative method is 5m-11, where m is the number of steps. The validity, accuracy, and efficiency of our proposed frozen Jacobian multistep iterative method is illustrated by solving fifteen IVPs and BVPs. It has been observed that, in all the test problems, with one exception in this paper, a single application of the proposed method is enough to obtain highly accurate numerical solutions. In addition, we present a comprehensive comparison of J-GL-C methods on a collection of test problems.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

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