Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
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. 

scholarly journals A MATHEMATICAL MODEL OF PAPER DRYING

2000 ◽  
Vol 5 (1) ◽  
pp. 26-31 ◽  
Author(s):  
J. Cepitis
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Moisture Transfer ◽  
Paper Sheet ◽  
Paper Drying ◽  
First Order ◽  
Heat And Moisture ◽  
Article 5 ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on a detailed transport phenomena considering both heat and moisture transfer have been offered in the article [5]. We apply this model to quickly moving paper sheet. The range of the moisture content correspond to the period of drying and only vapor movement in the web is possible. By averaging we have obtained the desired model as a system of two nonlinear first order ordinary differential equations.

Analysis of Mass Transfer during Loose Material’s Convective Drying

2011 ◽  
Vol 317-319 ◽  
pp. 2018-2021
Author(s):  
Xue Ping Wang ◽  
Wei Wei Cao ◽  
Yong Song ◽  
Zhen Wei Zhang
Keyword(s):  
Mass Transfer ◽  
Moisture Transfer ◽  
Convective Drying ◽  
Drying Rate ◽  
Drying Process ◽  
Moisture Migration ◽  
Phenomenological Equations ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Relationship

Abstract. The thesis focuses on how to get the mathematical model of mass transfer under some certain simplified conditions and how to gain the moisture content of materials under drying. In this process, authors utilized phenomenological equations of heat and moisture transfer and analyzed the relationship and cross effects between force and flow, which were about various kinds of heat and mass transfer. In addition, the authors also used computer simulation in drying process. The result of the study is that drying rate depends on the speed of the internal moisture migration. The conclusions of this thesis have great significance for selecting the dryer and in the actual production.

Continuous linear multistep method for the general solution of first order initial value problems for Volterra integro-differential equations

2018 ◽  
Vol 14 (5) ◽  
pp. 960-969
Author(s):  
Nathaniel Mahwash Kamoh ◽  
Terhemen Aboiyar
Keyword(s):  
General Solution ◽  
Approximation Method ◽  
Legendre Polynomial ◽  
Basis Function ◽  
Initial Value Problems ◽  
Block Method ◽  
Initial Value ◽  
Content Type ◽  
First Order ◽  
Predictor Corrector

Purpose The purpose of this paper is to develop a block method of order five for the general solution of the first-order initial value problems for Volterra integro-differential equations (VIDEs). Design/methodology/approach A collocation approximation method is adopted using the shifted Legendre polynomial as the basis function, and the developed method is applied as simultaneous integrators on the first-order VIDEs. Findings The new block method possessed the desirable feature of the Runge–Kutta method of being self-starting, hence eliminating the use of predictors. Originality/value In this paper, some information about solving VIDEs is provided. The authors have presented and illustrated the collocation approximation method using the shifted Legendre polynomial as the basis function to investigate solving an initial value problem in the class of VIDEs, which are very difficult, if not impossible, to solve analytically. With the block approach, the non-self-starting nature associated with the predictor corrector method has been eliminated. Unlike the approach in the predictor corrector method where additional equations are supplied from a different formulation, all the additional equations are from the same continuous formulation which shows the beauty of the method. However, the absolute stability region showed that the method is A-stable, and the application of this method to practical problems revealed that the method is more accurate than earlier methods.

scholarly journals FORMULATION OF BLOCK SCHEMES WITH LINEAR MULTISTEP METHOD FOR THE APPROXIMATION OF FIRST-ORDER IVPS

2020 ◽  
Vol 4 (3) ◽  
pp. 313-322
Author(s):  
Sunday Obomeviekome Imoni ◽  
D. I. Lanlege ◽  
E. M. Atteh ◽  
J. O. Ogbondeminu
Keyword(s):  
Basis Function ◽  
Initial Value Problems ◽  
Hermite Polynomials ◽  
Multistep Method ◽  
Linear Multistep Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order ◽  
Block Scheme ◽  
Multi Step Methods

ABSTRACT In this paper, formulation of an efficient numerical schemes for the approximation first-order initial value problems (IVPs) of ordinary differential equations (ODE) is presented. The method is a block scheme for some k-step linear multi-step methods (and) using the Hermite Polynomials a basis function. The continuous and discrete linear multi-step methods (LMM) are formulated through the technique of collocation and interpolation. Numerical examples of ODE have been examined and results obtained show that the proposed scheme can be efficient in solving initial value problems of first order ODE.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nemat Dalir
Keyword(s):  
Fluid Mechanics ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Second Order ◽  
Nonlinear Pdes ◽  
Initial Value ◽  
Exact Analytical Solutions ◽  
First Order

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

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