Autonomous Nonlinear Boundary-Value Problems for the Lyapunov Equation in the Hilbert Space

2021 ◽  
Author(s):  
D. S. Bihun ◽  
O. O. Pokutnyi ◽  
E. V. Panasenko
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Lyapunov Equation ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Multiplicity results by shooting reproducing kernel Hilbert space method for the catalytic reaction in a flat particle

2018 ◽  
Vol 17 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Babak Azarnavid ◽  
Elyas Shivanian ◽  
Kourosh Parand ◽  
Soudabeh Nikmanesh
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Reproducing Kernel ◽  
High Efficiency ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Well Performance ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

In this paper, a model of simultaneous mass and heat transfer within a porous catalyst in a flat particle is considered. A new modification of the shooting reproducing kernel Hilbert space (SRKHS) method is proposed, which is also capable of handling the system of nonlinear boundary value problems by employing Newtons method. The proposed method is a well-performance technique in both predicting and calculating multiple solutions of the nonlinear boundary value problems. Applying the SRKHS method shows that the mentioned model might admit multiple stationary solutions (unique, dual or triple solutions) depending on the values of the parameters of the model. Furthermore, the convergence of the method is proved and some numerical tests reveal the high efficiency of this new version of SRKHS method.

Sign in / Sign up

Export Citation Format

Share Document