Backward differentiation formulae with nonnegative coefficients for solving initial value problems

1992 ◽  
Vol 9 (3) ◽  
pp. 397-411 ◽  
Author(s):  
Kazufumi Ozawa
Keyword(s):  
Initial Value Problems ◽  
Initial Value ◽  
Nonnegative Coefficients ◽  
Backward Differentiation Formulae

scholarly journals Improved Two-Point Block Backward Differentiation Formulae for Solving First Order Stiff Initial Value Problems of Ordinary Differential Equations

2020 ◽  
Vol 3 (2) ◽  
pp. 200-209
Author(s):  
S Adee ◽  
VO Atabo
Keyword(s):  
Initial Value Problems ◽  
Taylor Series Expansion ◽  
Kutta Method ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
New Methods ◽  
Runge Kutta Method ◽  
Backward Differentiation Formulae ◽  
Convergence And Stability Analysis

Two numerical methods- I2BBDF2 and I22BBDF2 that compute two points simultaneously at every step of integration by first providing a starting value via fourth order Runge-Kutta method are derived using Taylor series expansion. The two-point block schemes are derived by modifying the existing I2BBDF (5) method of Mohamad et al., (2018). Convergence and stability analysis of the new methods are established with the methods being of order two and A-stable in both cases. Despite the very low order of the new methods, the accuracy of these methods on some stiff initial value problems in the literature proves their superiority over existing methods of higher orders such as I2BBDF(5), BBDF(5), E2OSB(4) among others.

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 Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2023
Author(s):  
Christopher Nicholas Angstmann ◽  
Byron Alexander Jacobs ◽  
Bruce Ian Henry ◽  
Zhuang Xu
Keyword(s):  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Integral Transform ◽  
Initial Value ◽  
Intrinsic Nature ◽  
Recent Interest ◽  
Special Cases ◽  
Singular Kernels

There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities.

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