High order implicit method for odes stiff systems
Copyright policy )High order implicit method for odes stiff systems
A doubly implicit A-stable difference scheme with order six is proposed for the numerical solution of stiff systems of ordinary differential equations (ODEs). The integration step is selected according a difference scheme derived from the proposed method and a one step scheme of fourth order of approximation. Numerical tests are also included. The tests problems are the Kreiss problem and a chemical kinetic problem. Comparisons results of the proposed method with the Gear's backward differentiation formula method of 6-th order shows that efficiencies of both methods coincide approximately.
- Volgograd State University Russian Federation
Finite difference and finite volume methods for ordinary differential equations, backward differentiation formula method, stiff systems, Finite difference methods applied to problems in thermodynamics and heat transfer, Nonlinear ordinary differential equations and systems, chemical kinetic, Numerical methods for initial value problems involving ordinary differential equations, Chemical kinetics in thermodynamics and heat transfer, implicit method, step size control, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical tests, comparison, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Kreis problem, difference methods, A-stability, Stability and convergence of numerical methods for ordinary differential equations
Finite difference and finite volume methods for ordinary differential equations, backward differentiation formula method, stiff systems, Finite difference methods applied to problems in thermodynamics and heat transfer, Nonlinear ordinary differential equations and systems, chemical kinetic, Numerical methods for initial value problems involving ordinary differential equations, Chemical kinetics in thermodynamics and heat transfer, implicit method, step size control, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical tests, comparison, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Kreis problem, difference methods, A-stability, Stability and convergence of numerical methods for ordinary differential equations
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