Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems

In this article an innovative technique named as Optimal Homotopy Asymptotic Method has been explored to treat system of KdV equations computed from complex KdV equation. By developing special form of initial value problems to complex KdV equation, three different types of semi analytic complextion solutions fromcomplexKdVequation have been achieved. First semi analytic position solution received fromtrigonometric form of initial value problem, second is semi analytic negation solution received by hyperbolic form of initial value problem and third one is special type of semi analytic solution expressed by the combination of trigonometric and hyperbolic functions. It was proved that only first order OHAM solution is accurate to the closed-form solution.

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Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

Mathematical Problems in Engineering ◽

10.1155/2013/498902 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 9

Author(s):

N. Ratib Anakira ◽

A. K. Alomari ◽

I. Hashim

Keyword(s):

Differential Equations ◽

Asymptotic Method ◽

Delay Differential Equations ◽

Perturbation Methods ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Initial Value ◽

Optimal Homotopy Asymptotic Method ◽

Delay Differential ◽

First Time

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

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Some algebraic approach for the second Painleve equation using the optimal homotopy asymptotic method (OHAM)

Сибирский журнал вычислительной математики ◽

10.15372/sjnm20180207 ◽

2018 ◽

Keyword(s):

Asymptotic Method ◽

Algebraic Approach ◽

Painlevé Equation ◽

Optimal Homotopy Asymptotic Method ◽

Painleve Equation ◽

Second Painlevé Equation

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Numerical Solution of Fuzzy Initial Value Problems by Fourth Order Runge-Kutta Method Based on Contraharmonic Mean

Indian Journal Of Applied Research ◽

10.15373/2249555x/apr2013/111 ◽

2011 ◽

Vol 3 (4) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

R. Gethsi Sharmila ◽

◽

E. C. Henry Amirtharaj

Keyword(s):

Numerical Solution ◽

Fourth Order ◽

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Contraharmonic Mean ◽

Runge Kutta

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Mathematical Models of Papermaking

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2001.6.1.15221 ◽

2001 ◽

Vol 6 (1) ◽

pp. 9-19 ◽

Cited By ~ 1

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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