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B-convergence of Additive Runge-Kutta Methods for Stiff Problems

Author: YueChao
Tutor: XiaoAiGuo
School: Xiangtan University
Course: Computational Mathematics
Keywords: Superimposed Runge-Kutta method Fractional step method Stiffness problem B - debt-collection of The stability of the weak algebraic (θ, (p -), (Q - )) - Algebra stable Diagonal stability ANS- stable
CLC: O241.81
Type: Master's thesis
Year: 2008
Downloads: 43
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Abstract


Rigidity problem is a special class of differential equations initial value problem , with a wide range of application background . Runge-Kutta method is a commonly used method for Differential Equations . For rigid , we generally use the implicit Runge-Kutta methods , so that we can get a high-precision numerical solution , but to the great amount of computation . Therefore , we often used to calculate the diagonal implicit Runge-Kutta method to reduce the amount of calculation . In recent years , more and more scholars can be divided into two parts and even more rigid problem generated strong interest . For such rigid problem solving , in order to reduce the amount of computation , we superimposed Runge-Kutta method : For rigid part of the implicit Runge-Kutta method ; explicit Runge-Kutta method can be used for the non-rigid part . B - convergence order of this paper is to use overlay Runge-Kutta method to solve the rigid algebra angle stable overlay Runge-Kutta method for K 0,0 initial value problem Runge-Kutta method not less than the order level , and obtain a sufficient condition for the best B- convergence of the method is a higher order than the order level , weak algebra also proved stable and diagonally stable ( or the ANS- stable ) superimposed on the K 0 , ω the initial value problem , the best B - convergence order is not lower than the order level , and obtain a sufficient condition for the best B- convergence of the method is a higher order than the order level . Also prove a fractional step method Runge-Kutta method K 0,0 class K 0 , ω the initial value problem B- convergence . Finally, we prove (θ, (?), (?)) - Algebraically stable and diagonally stable (or ANS- stable ) superimposed Runge-Kutta method about K σ, τ class initial value problem of the best B- convergence order is not less than the order level and sufficient condition for the best B- convergence of the method is a higher order than the order level . Also prove ( θ , ( ? ) ( ? )) - Algebraically stable Runge-Kutta methods superimposed on the the K φ Runge- monotonicity and fractional step method , the initial value problem ( ? ) Kutta method at K σ , τ B - convergence of the initial value problem .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Ordinary Differential Equations
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