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Comparison of some runge kutta methods for solving differential algebraic equations
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Mục lục
Introduction
Differential-algebraic equations
Definition of DAEs
Index of a DAE
Runge-Kutta methods
Formulation of Runge-Kutta methods
Classes of Runge-Kutta methods
Implicit RK methods and half-explicit RK methods for semi-explicit DAEs of index 2
Introduction
Implicit Runge-Kutta methods
Formula of implicit Runge-Kutta methods
Convergence of implicit Rung-Kutta methods
Half-explicit Rung-Kutta methods
Formula of half-explicit Runge-Kutta methods
Discussion of the convergence
Partitioned HERK methods for semi-explicit DAEs of index 2
Introduction
Partitioned half-explicit Runge-Kutta methods
Definition of partitioned half-explicit RK method
Existence and influence of perturbations
Convergence of partitioned half-explicit Runge-Kutta methods
Construction of partitioned half-explicit Runge-Kutta methods
Methods of order up to 4
Methods of order 5 and 6
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