scholarly journals DEGENERATE MATRIX METHOD WITH CHEBYSHEV NODES FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1999 ◽  
Vol 4 (1) ◽  
pp. 51-57
Author(s):  
T. Cirulis ◽  
O. Lietuvietis
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Newton Method ◽  
Chebyshev Polynomials ◽  
Matrix Method ◽  
Discrete Problem ◽  
Chebyshev Nodes ◽  
Systems Of Differential Equations ◽  
Degenerate Matrix

One of the simplest schemes of the degenerate matrix method with nodes as zeroes of Chebyshev polynomials of the second kind is considered. Performance of simple iterations and some modifications of Newton method for the discrete problem is compared.

scholarly journals DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998 ◽  
Vol 3 (1) ◽  
pp. 45-56
Author(s):  
T. Cîrulis ◽  
O. Lietuvietis
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Iteration Procedure ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Systems Of Differential Equations ◽  
Runge Kutta ◽  
Degenerate Matrix

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given.

scholarly journals Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440
Author(s):  
Olusola Akinyele
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Practical Stability ◽  
Lipschitz Stability ◽  
Comparison Result ◽  
Systems Of Differential Equations ◽  
New Concepts ◽  
Perturbed Systems

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts ofϕ0-uniform Lipschitz stability and(λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.

MULTISTEP DEGENERATE MATRIX METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS

2001 ◽  
Vol 6 (1) ◽  
pp. 58-67
Author(s):  
T. Cirulis ◽  
D. Cirule ◽  
O. Lietuvietis
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Complex Plane ◽  
Matrix Method ◽  
Stability Function ◽  
The Stability ◽  
Nonuniformly Distributed Nodes ◽  
Degenerate Matrix ◽  
Residue Theory

Two of the simplest general schemes of the degenerate matrix method in the multistep mode are considered. The stability function for these methods is computed by the residue theory in the complex plane. Performances of uniformly and nonuniformly distributed nodes in the standardized interval are compared.

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