scholarly journals Application of Mathematica Software to Solve Pulp Washing Model

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jitender Kumar ◽  
Ishfaq A. Ganaie ◽  
Vijay K. Kukreja
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Length ◽  
Separation Of Variables ◽  
Packed Beds ◽  
Pulp Fibers ◽  
Partial Differential ◽  
Mathematica Software

The removal of the bulk liquor surrounding the pulp fibers using less concentrated liquor is known as pulp washing. In the present study, a pulp washing model involving diffusion-dispersion through packed beds of finite length is presented. Separation of variables is applied to solve system of governing partial differential equations and the resulting equations are solved using Mathematica. Results from the present case are compared with those of previous investigators. The present case is giving better results than the previous investigators.

Beam Vibrations With Time-Dependent Boundary Conditions

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Time Dependent ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

scholarly journals Similarity Solutions of Partial Differential Equations in Probability

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Mario Lefebvre
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Processes ◽  
Separation Of Variables ◽  
Similarity Solutions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Generalized Fourier Series ◽  
Dimensional Diffusion ◽  
Concentric Circles

Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series.

scholarly journals Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Abdolamir Karbalaie ◽  
Hamed Hamid Muhammed ◽  
Bjorn-Erik Erlandsson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Separation Of Variables ◽  
General Purpose ◽  
New Method ◽  
Fractional Partial Differential Equations ◽  
Mathematical Methods ◽  
Partial Differential ◽  
Separation Of Variables Method ◽  
Linear And Nonlinear

A new method proposed and coined by the authors as the homo-separation of variables method is utilized to solve systems of linear and nonlinear fractional partial differential equations (FPDEs). The new method is a combination of two well-established mathematical methods, namely, the homotopy perturbation method (HPM) and the separation of variables method. When compared to existing analytical and numerical methods, the method resulting from our approach shows that it is capable of simplifying the target problem at hand and reducing the computational load that is required to solve it, considerably. The efficiency and usefulness of this new general-purpose method is verified by several examples, where different systems of linear and nonlinear FPDEs are solved.

Solutions of Certain Fractional Partial Differential Equations

2021 ◽  
Vol 20 ◽  
pp. 504-507
Author(s):  
Alsauodi Maha ◽  
Alhorani Mohammed ◽  
Khalil Roshdi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Tensor Product ◽  
Banach Spaces ◽  
Separation Of Variables ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

In this paper we find certain solutions of some fractional partial differential equations. Tensor product of Banach spaces is used where separation of variables does not work.

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