Evolutionary derivation of Runge–Kutta pairs for addressing inhomogeneous linear problems

被引：0
作者：
T. E. Simos
Ch. Tsitouras
机构：
[1] Chengdu University of Information Technology,College of Applied Mathematics
[2] South Ural State University,Data Recovery Key Laboratory of Sichuan Province
[3] Neijiang Normal University,Section of Mathematics, Department of Civil Engineering
[4] Democritus University of Thrace,General Department
[5] National and Kapodistrian University of Athens,undefined
来源：
Numerical Algorithms | 2021年 / 87卷
关键词：
Initial value problem; Linear inhomogeneous; Runge–Kutta; Order conditions; Differential evolution; 65L05;
D O I：
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中图分类号：
学科分类号：
摘要：
Two new Runge–Kutta (RK) pairs of orders 6(4) and 7(5) are presented for solving numerically the inhomogeneous linear initial value problems with constant coefficients. These new pairs use only six and eight stages per step respectively. Six stages are needed for conventional Runge–Kutta pairs of orders 5(4) while for such a pair of orders 6(5) we use eight stages. Thus, our proposal is an improvement and it is achieved since the set of order conditions is smaller in the case of interest here. Since traditional simplifications for derivation of Runge–Kutta methods do not apply for this reduced set, we proceed using the differential evolution technique for solving it. We finalize by performing tests over some relevant problems with very pleasant results.
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页码：511 / 525
页数：14
相关论文
共 69 条
[1]  
Butcher JC(1964)Implicit Runge-Kutta processes Math. Comput. 18 50-64
[2]  
Butcher JC(1964)On Runge-Kutta processes of high order J. Austral. Math. Soc. 4 179-194
[3]  
Dormand JR(1989)Global error estimation with Runge-Kutta triples Comput. Maths. Appl. 18 835-846
[4]  
Lockyer MA(1980)A family of embedded Runge-Kutta formulae J. Comput. Appl. Math. 6 19-26
[5]  
McGorrigan NE(1969)Error estimates for Runge? Kutta type solutions of systems of ordinary differential equations Comput. J 12 166-170
[6]  
Prince PJ(1978)The efficient solution of linear constant-coefficient systems of differential equations Simulation 30 129-133
[7]  
Dormand JR(2004)Symbolic derivation of Runge-Kutta order conditions J. Symbolic Comput. 37 311-327
[8]  
Prince PJ(2005)Explicit exponential Runge–Kutta methods for semilinear parabolic problems SIAM J. Numer. Anal. 43 1069-1090
[9]  
England R(2016)Four stages symmetric two-step p-stable method with vanished phase-lag and its first, Second, Third and Fourth derivatives Appl. Comput. Math. 15 220-238
[10]  
Enright WH(2019)Explicit, semi-symmetric, hybrid, six-step, eighth order methods for solving y$^{\prime \prime }=$′′ =f(x,y) Appl. Comput. Math. 18 396-304
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