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2003•核工业西南物理研究院年报：英文版Requires access

Semi-implicit Runge.Kutta Method for Solving Stiff Ordinary Differential Equations

LONGYongxing, MOUZongze, DONGJiaqi, ZHAOHuaiguo

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Abstract

Runge-Kutta method is widely applied to solve the initial value problem of ordinary differential equations. The implicitRunge-Kutta with better numerical stability for the numerical integration of stiff differential systems,but the formulate has traditionally been on solving the nonlinear equations resulting from a modified Newton iteration in every time.Semi-implicit formulate have the major computationally advantage that it is necessary to solve only linear systems of algebraic equations to find the Ka.

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What this paper is about

Runge-Kutta method is widely applied to solve the initial value problem of ordinary differential equations. The implicitRunge-Kutta with better numerical stability for the numerical integration of stiff differential systems,but the formulate has traditionally been on solving the nonlinear equations resulting from a modified Newton iteration in every time.Semi-implicit formulate have the major computationally advantage that it is necessary to solve only linear systems of algebraic equations to find the Ka.

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Available abstract

Runge-Kutta method is widely applied to solve the initial value problem of ordinary differential equations. The implicitRunge-Kutta with better numerical stability for the numerical integration of stiff differential systems,but the formulate has traditionally been on solving the nonlinear equations resulting from a modified Newton iteration in every time.Semi-implicit formulate have the major computationally advantage that it is necessary to solve only linear systems of algebraic equations to find the Ka.

Key concepts: Runge–Kutta methods, Backward differentiation formula, Mathematics, L-stability, Numerical methods for ordinary differential equations, Explicit and implicit methods, Differential algebraic equation, Nonlinear system

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