Optimal Difference Schemes for Linear Initial Value Problems

1973 ◽  
Vol 10 (6) ◽  
pp. 983-1009 ◽  
Author(s):  
C. A. Micchelli ◽  
W. L. Miranker
Keyword(s):  
Initial Value Problems ◽  
Difference Schemes ◽  
Initial Value

scholarly journals Solving the Sturm-Liouville problem by three-point difference schemes of high order of accuracy

2021 ◽  
pp. 186-190
Author(s):  
Andrii Kunynets ◽  
Myroslav Kutniv ◽  
Nadia Khomenko
Keyword(s):  
Initial Value Problems ◽  
Numerical Experiments ◽  
Liouville Problem ◽  
High Order ◽  
Difference Schemes ◽  
Initial Value ◽  
Order Of Accuracy ◽  
Sturm Liouville ◽  
High Order Of Accuracy ◽  
Iterative Newton Method

For the solving Sturm-Liouville problem, three-point difference schemes of high order of accuracy on a nonuniform grid are constructed. It is shown that the coefficients of these schemes are expressed in terms of solutions of two auxiliary initial value problems. An estimate of the accuracy of three-point difference schemes is obtained and an iterative Newton method is proposed to determine their solution. Numerical experiments confirm theoretical conclusions.

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. 

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