Laplace Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Partial Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Arun Kumar ◽  
Ram Dayal Pankaj
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Weak Nonlinearity ◽  
Partial Differential ◽  
New Approach ◽  
Laplace Decomposition Method

Analytical and numerical solutions are obtained for coupled nonlinear partial differential equation by the well-known Laplace decomposition method. We combined Laplace transform and Adomain decomposition method and present a new approach for solving coupled Schrödinger-Korteweg-de Vries (Sch-KdV) equation. The method does not need linearization, weak nonlinearity assumptions, or perturbation theory. We compared the numerical solutions with corresponding analytical solutions.

Pressure Behavior During Polymer Flow in Petroleum Reservoirs

1982 ◽  
Vol 104 (2) ◽  
pp. 149-156 ◽  
Author(s):  
Chi U. Ikoku ◽  
H. J. Ramey
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
State Equations ◽  
Partial Differential ◽  
Dimensionless Radius ◽  
Dimensionless Pressure

This paper presents solutions of the nonlinear partial differential equation using the Douglas-Jones predictor-corrector method for the numerical solution of nonlinear partial differential equations. The results are presented in tabular form and as semilogarithmic and log-log type-curve graphs. Graphs of dimensionless pressure versus dimensionless radius also are presented. Compared to results from analytical solutions of the linear partial differential equation, the graphs have the same shape. The error introduced by the linearizing approximation is small for many values of the flow behavior index, n, and decreases as n tends to unity. Dimensionless pressure is a linear function of dimensionless radius to the power (1–n), near the well, as predicted by the steady-state equations. Also radius of investigation equation derived analytically agrees with results from numerical solutions.

scholarly journals Double Laplace Decomposition Method and Finite Difference Method of Time-fractional Schrödinger Pseudoparabolic Partial Differential Equation with Caputo Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mahmut Modanli ◽  
Bushra Bajjah
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Caputo Derivative ◽  
Decomposition Method ◽  
Linear Time ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Partial Differential ◽  
Laplace Decomposition Method

In this paper, an initial-boundary value problem for a one-dimensional linear time-dependent fractional Schrödinger pseudoparabolic partial differential equation with Caputo derivative of order α ∈ 0,1 is being considered. Two strong numerical methods are employed to acquire the solutions to the problem. The first method used is the double Laplace decomposition method where closed-form solutions are obtained for any α ∈ 0,1 . As the second method, the implicit finite difference scheme is applied to obtain the approximate solutions. To clarify the performance of these two methods, numerical results are presented. The stability of the problem is also investigated.

Akbari-Ganji's Method

2017 ◽  
pp. 246-273
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Chemical Engineering ◽  
Solid Mechanics ◽  
Nonlinear Partial Differential Equation ◽  
The Other ◽  
Partial Differential ◽  
New Approach

The nonlinear partial differential equation governing on the mentioned system has been investigated by a simple and innovative method which we have named it Akbari-Ganji's Method or AGM. It is notable that this method has been compounded by Laplace transform theorem in order to covert the partial differential equation governing on the afore-mentioned system to an ODE and then the yielded equation has been solved conveniently by this new approach (AGM). One of the most important reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in heat transfer science but also in different fields of study such as solid mechanics, fluid mechanics, chemical engineering, etc. in comparison with the other methods is as follows: Obviously, according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, this method can create additional new boundary conditions in regard to the own differential equation and its derivatives. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods.

scholarly journals Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Xiao-Feng Yang ◽  
Yi Wei
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Expansion Method ◽  
Partial Differential ◽  
The Kdv Equation ◽  
Compatible Condition ◽  
Ode Method ◽  
Bilinear Equation

The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. The KdV equation, Burgers equation, Boussinesq equation, and Sawada-Kotera equation are chosen to illustrate the validity of our method. We find that the underlying relation among the G′/G-expansion method, Hirota’s method, and HB method is a bilinear equation. The proposed method is also a standard and computable method, which can be generalized to deal with other types of NLPDE.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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