Pressure Behavior During Polymer Flow in Petroleum Reservoirs

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.

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

International Journal of Engineering Technologies and Management Research ◽

10.29121/ijetmr.v5.i1.2018.42 ◽

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

ISRN Computational Mathematics ◽

10.5402/2012/423469 ◽

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.

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

Journal of Education College Wasit University ◽

10.31185/eduj.vol1.iss25.137 ◽

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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A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100023197 ◽

1947 ◽

Vol 43 (1) ◽

pp. 50-67 ◽

Cited By ~ 1578

Author(s):

J. Crank ◽

P. Nicolson

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Heat Conduction ◽

Numerical Evaluation ◽

Numerical Solutions ◽

Linear Partial Differential Equation ◽

Practical Method ◽

Partial Differential ◽

Image Position ◽

Internal Generation

This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equationwheresubject to the boundary conditionsA, k, q are known constants.Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).

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