Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations

2015 ◽  
Author(s):  
Mohammed ALshbool ◽  
Ishak Hashim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bernstein Polynomials ◽  
Stiff System

scholarly journals Stiff systems of ordinary differential equations. III. Partially stiff systems

1982 ◽  
Vol 23 (3) ◽  
pp. 310-331 ◽  
Author(s):  
J. J. Mahony ◽  
J. J. Shepherd
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Solution Space ◽  
Homogeneous System ◽  
Stiff Systems ◽  
Stiff System ◽  
Specific System ◽  
Small Positive Parameter ◽  
Image Position

AbstractThe partially stiff system of ordinary differential equationsis studied by the methods developed in the earlier papers in this series. Here e is a small positive parameter, x and y are n- and m-vectors respectively, and A is nonsingular. A useful basis for the solution space of the homogeneous system is constructed and the method of variation of parameters is used to obtain useful representations of all solutions. Sufficient conditions are derived under which the formal approximationis close to the actual solution. it is found that purely imaginary eigenvalues for A require more stringent requirements for the formal technique to be valid. A brief discussion of the case when A is singular shows that there are a great number of possibilities requiring consideration for a general theory. it is suggested that local computation of such cases is likely to be the most effective weapon for any specific system.

scholarly journals Numerical solution of the first order nonlinear differen-tial equations with the mixed nonlinear conditions by using PLSM(comparison with Bernstein polynomials method)

2019 ◽  
Vol 29 ◽  
pp. 01014
Author(s):  
Marioara Lăpădat ◽  
Mohsen Razzaghi ◽  
Mădălina Sofia Paşca
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Least Squares ◽  
Ordinary Differential Equations ◽  
Least Squares Method ◽  
Bernstein Polynomials ◽  
Approximate Solutions ◽  
Nonlinear Ordinary Differential Equations ◽  
First Order ◽  
Approximate Polynomial

We use the Polynomial Least Squares Method (PLSM), which allows us to compute analytical approximate polynomial solutions for nonlinear ordinary differential equations with the mixed nonlinear conditions. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using Bernstein polynomials method.

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