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

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 Transient-False Method for Solving System of Nonlinear Partial Differential Equations

2018 ◽  
Vol 1 (25) ◽  
pp. 509-522
Author(s):  
. Ali Khalaf Hussain
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Linear Algebraic Equations

          In this paper we study the false transient method  to  solve and transform a system of non-linear partial differential equations which can be solved using finite-difference method and give some problems which have a good results compared with the exact solution, whereas this method was used to transform the nonlinear partial differential equation to a linear partial differential equation which can be solved by using the alternating-direction implicit method after using the ADI method. The system of linear algebraic equations could be obtained and can be solved by using MATLAB.

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