|
|
Numerical solution of index-2 differenial-algebraic equations
Kroulíková, Tereza ; Opluštil, Zdeněk (referee) ; Zatočilová, Jitka (advisor)
This bachelor´s thesis deals with numerical solution of differential-algebraic equations. At first these equations are described theoretically and their basic properties are presented. Main attention is paid to index and the most used indexes are described in details. Then the thesis concentrates on numerical solution of Hessenberg forms index-2 differential-algebraic equations. Implicit Runge-Kutta methods and backward differentiation formulas are derived. Those are used for solution of index-2 differential-algebraic equations.
|
|
|
Oscillations in mechanical systems with implicit constitutive relations.
Babováková, Jana ; Pražák, Dalibor (advisor) ; Janovský, Vladimír (referee)
We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.
|
|
|
Oscillations in mechanical systems with implicit constitutive relations.
Babováková, Jana ; Pražák, Dalibor (advisor) ; Janovský, Vladimír (referee)
We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.
|
|
|
Numerical solution of index-2 differenial-algebraic equations
Kroulíková, Tereza ; Opluštil, Zdeněk (referee) ; Zatočilová, Jitka (advisor)
This bachelor´s thesis deals with numerical solution of differential-algebraic equations. At first these equations are described theoretically and their basic properties are presented. Main attention is paid to index and the most used indexes are described in details. Then the thesis concentrates on numerical solution of Hessenberg forms index-2 differential-algebraic equations. Implicit Runge-Kutta methods and backward differentiation formulas are derived. Those are used for solution of index-2 differential-algebraic equations.
|
guest ::
